TOPICS
Search

Incomplete Entries

Any assistance in providing additional information for the following items would be greatly appreciated. In many cases, the missing portions are article names, volume numbers, page ranges or ending pages, publication city, etc. Where possible, the needed information is indicated explicitly, e.g., in the form [VOLUME?]. Note that in some cases, the information missing may not be explicitly indicated, but may instead simply be a copy of a citation in its current form.

A typical journal citation should be of the form

        Author, Initials. "Title." Journal Volume, [Beginning Page]-[Ending Page], Year.

A typical book citation should be of the form

        Author, Initials. Title. City: Publisher, [Page Range], Year.

In other cases, missing information may be verifying an equation, adding a figure, etc. In such cases, the following may contain only a cryptic short-hand note from the author to himself. Over time, these cryptic notes will be replaced with more easily decipherable information requests. In the meantime, please send information to the MathWorld team.

120-Cell (Debroni, S.; Delisle, E.; Myrvold, W.; Sethi, A.; Whitney, J.; Woodcock, J.; Fowler, P. W.; de La La Vaissière, B.; and Deza, M. "Maximum Independent Sets of the 120-Cell and Other Regular Polyhedra." To appear in Ars Mathematica Contemporanea.)

600-Cell (Debroni, S.; Delisle, E.; Myrvold, W.; Sethi, A.; Whitney, J.; Woodcock, J.; Fowler, P. W.; de La La Vaissière, B.; and Deza, M. "Maximum Independent Sets of the 120-Cell and Other Regular Polyhedra." To appear in Ars Mathematica Contemporanea.)

Abelian Differential (any reference)

Alexander's Horned Sphere (Albers, D. J. Illustration accompanying "The Game of 'Life.' " Math Horizons, p. 9, Spring 1994)

Amicable Pair (Paganini, B. N. I. [TITLE?] Atti della R. Accad. Sc. Torino 2, 362 [ENDING PAGE?], 1866-1867.)

Anomalous Cancellation (Moessner, A. Scripta Math. 19. [cited in Wells] Moessner, A. Scripta Math. 20. [cited in Wells])

Antipode (add figure)

Arbelos (Boas, H. P. "Reflections on the Arbelos." Preprint based on the Nineteenth Annual Rose-Hulman Undergraduate Mathematics Conference, March 15, 2002. Oct. 26, 2004.)

Archimedean Valuation (C+1 appears to be wrong)

Augmentation (Graziotti, U. Polyhedra, the Realm of Geometric Beauty. San Francisco, CA: 1962.)

Ax-Kochen Isomorphism Theorem (nonprincipal maximal filter)

Baguenaudier (Kauffman, L. H. "Tangle Complexity and the Topology of the Chinese Rings." In Mathematical Approaches to Biomolecular Structure and Dynamics. New York: Springer-Verlag, pp. 1-10, 1996)

Baker-Campbell-Hausdorff Series (Dynkin, E. B. [TITLE?] Math. Rev. 11, 80 [ENDING PAGE?], 1949.; Reutenauer, C. Ch. 3 in Free Lie Algebras. New York: Oxford University Press, [PAGE RANGE?], 1993.;)

Bang's Theorem (Bang, A. S. [TITLE?] Tidskrift f. Math., [VOL?], p. 48 [PAGE RANGE], 1897. Gehrke. [INITIALS?] [TITLE?] Tidskrift for Math. [VOL?], p. 84 [PAGE RANGE], 1897. In Bang's (1951) theorem, what is w in w(K)?)

Bauer's Identical Congruence (Bauer. Nouvelles annales 2, 256-264, 1902.; Hardy, G. H. and Wright, E. M. J. London Math. Soc. 9, 38-41 and 240, 1934.;)

BBP-Type Formula (Borwein, J. M. and Chamberland, M. "A Golden Example." Unpublished manuscript.; Cloitre, B. "A BBP Formula for pi^2 in Golden Base." Unpublished manuscript.)

Benham's Wheel (Benham 1894; Brücke 1864; Finnegan and Moore 1895; Helmholtz 1856; Kunsemüller, J. Meyers Lexikon der Technik und der exakten Naturwissenschaften, Bd. 1. A - E. [CITY?] Fischer Taschenbuch Verlag, [PAGES?] 1970)

Bessel's Correction (Gauss, C. F. "Theoria combinationis obsevationum erroribus minimis obnoxiae." Werke, Bd. 4. Göttingen, [PUBLISHER?] p. 1 [PAGE RANGE], 1823.)

Bialtitude (add figure)

Bicentric Quadrilateral (Davis, M. A. Educ. Times 32.)

Binomial Sums (Almkvist, G.; Krattenthaler, C.; and Petersson, J. "Some New Formulas for Pi." Manuscript, 2001.; sloane: 2/3, 4/3, 10/3, 32/3, [need more terms]; sloane: 2/9, 10/27, 74/81, [need more terms]; sloane: 2/25, 81/625, 561/3125, [need more terms]; sloane: -6/125, -18/3125, 42/15625, [need more terms]; sloane: 11/250, 79/3125, 673/31250, [need more terms];)

Binormal Vector (add figure)

Bôcher's Theorem (Bôcher. "The Location of Critical Points." Amer. Math. Soc. Colloq. Publ. 34, 1950.)

Boolean Function (what do monotonic and monotonic increasing mean in this context?; Shapiro. "On the Counting Problem for Monotone Boolean Functions." Comm. Pure Appl. Math. 23, 299-312, 1970.)

Box Integral (Bailey, D. H.; Borwein, J. M.; and Crandall, R. E. "Box Integrals." Preprint. Apr. 3, 2006.)

Braikenridge-Maclaurin Construction (add figure)

Breeder (make sense of last sentence)

Bridge Knot (Complete number of bridge knots of 5-9 crossings)

Bridge Number (make sure I mean 05-002 here; was 05-05)

Brocard's Problem (Berndt, B. C. and Galway, W. F. "On the Brocard-Ramanujan Diophantine Equation n!+1=m^2." Submitted.; Ramanujan 1913; Gerard 1906)

Brun's Constant (Segal, B. "Generalisation du théorème de Brun." Dokl. Akad. Nauk SSSR [VOLUME?], 501-507, 1930.;)

Burridge-Knopoff Model (Burridge, R. and Knopoff, L. Bull. Seis. Soc. Amer. 57, 341, 1967.; de Sousa Vieira, M. Phys. Rev. Lett. 82, 201, 1999.; Ferguson, C. D.; Klein, W.; and Rundle., J. B. Computers Physics 12, 34 1998.; Hähner, P. and Drossinos, Y. Physica A 260, 391, 1998.; Place, D. and Villedieu, P. J. Comput. Phys. 150, 332,1999.; Xu, H.-J and Knopoff, L. Phys. Rev. E 50, 3577, 1994.;)

Cage Graph (sloane: 6,10,30,42 sloane: 7,12,40,62 sloane: 8,14,50,90)

Carmichael's Conjecture (Cipra reference)

Casey's Theorem (more figures)

Cassini Ovals (Gosper says it is only the critical case where the ovals unite)

Catacaustic (Borovikov, V. A. and Kinber, B. Y. [TITLE?] Geometrical Theory of Diffraction. London: Institute of Electrical Engineering, 1994.; Bruce, J. W.; Giblin, P. G.; and Gibson, C. G. [TITLE?] Proc. Symposia Pure Math. 40/1, 179 [ENDING PAGE?], 1983.; Bruce, J. W.; Giblin, P. G.; and Gibson, C. G. [TITLE?] Topology 21, 179 [ENDING PAGE?], 1982.; Bruce, J. W.; Giblin; P. G.; and Gibson, C. G. [TITLE?] Amer. Math. Monthly 88, 651 [ENDING PAGE?], 1981.; Cornbleet, S. [TITLE?] Microwave and Geometrical Optics. London: Academic Press, 1994.; Ehlers, J. and Newman, E. T. [TITLE?] J. Math. Phys. 41, 3344 [ENDING PAGE?], 2000.; Georgiou, C.; Hasanis, T.; Koutroufiotis, D. [TITLE?] Geom. Dedicata 28, 153 [ENDING PAGE?], 1988.; Giblin, P. J. and Kingston, J. G. [TITLE?] Quart. J. Math Oxford 37, 17 [ENDING PAGE?], 1986.; Hairer, E. and Wanner, G. [TITLE?] Analysis by Its History. New York: Springer-Verlag, 1996.; Hartman, P. and Valentine, F. A. [TITLE?] Duke Math. J. 26, 373 [ENDING PAGE?], 1959.; Knill, O. [TITLE?] Elem. Math. 53, 89 [ENDING PAGE?], 1998.; Loe, B. L. and Beagley, N. [TITLE?] Coll. Math. J. 28, 277 [ENDING PAGE?], 1997.; Porteous, I. R. [TITLE?] Geometric Differentiation for the Intelligence of Curves and Surfaces. Cambridge, England: Cambridge University Press, 1994.; Poston, T. and Stewart, I. [TITLE?] Catastrophe Theory and Its Application. London: Pitman, 1978.; Schupp, H. and Dabrock, H. [TITLE?] Höhere Kurven. Mannheim, Germany: BI, 1995.)

Catalan's Constant (sloane: 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, Bresse (1867) [from http://functions.wolfram.com/Constants/I/introductions/ClassicalConstants/01/])

Cauchy-Frobenius Lemma (Cauchy, A. "Mémoire sur diverses propriétés remarquables des substitutions régulières ou irrégulières, et des systémes de substitutiones conjugées." Comptes Rendus Acad. Sci. Paris 21, 835, 1845.;)

Chaos (Calogero, F.; Gomez-Ullate, D.; Santini, P. M.; and Sommacal, M. "Towards a Theory of Chaos as Travel on a Riemann Surface. I." In preparation.; Calogero, F.; Gomez-Ullate, D.; Santini, P. M.; and Sommacal, M. "Towards a Theory of Chaos as Travel on a Riemann Surface. II." In preparation.;)

Character Table (finish tables)

Chebyshev (Clenshaw, C. W. Mathematical Tables, Vol. 5: Chebyshev Series for Mathematical Functions. Department of Scientific and Industrial Research.)

Chess (Dawson, T. R. "A Surprise Correction." The Fairy Chess Review 6, 44, 1946; Cunningham 1889; Fabel, K. Die Schwalbe 89, 284-285, 1935.; check: Peterson 10.120)

Chevalley Groups (add correct restrictions on parameters n and q)

Chinese Hypothesis (Jeans, J. H. Messenger Math. 27, 1897-98.; Needham, J. Ch. 19 in Science and Civilisation in China, Vol. 3.)

Chió Pivotal Condensation (Hermite 1859)

Circle Covering by Arcs (Whitworth, W. A. DCC Exercises in Choice and Chance. 1897.)

Circle Packing (Bowers, P. L. and Stephenson, K. "Uniformizing Dessins and Belyĭ Maps via Circle Packing." Preprint.; Collins, C. R. and Stephenson, K. "A Circle Packing Algorithm." Preprint.)

Circle Power (Clifford. Collected Mathematical Papers. 1882.)

Circles-and-Squares Fractal (any reference)

Circumcevian Triangle (Kimberling, C. "Transfigured Triangle Geometry." Preprint. Mar. 5, 2005.)

Cissoid (add figure)

Class 1 Graph (Jarnicki et al. 2015. Preprint)

Complex Matrix (Hwang, C. R. "A Brief Survey on the Spectral Radius and the Spectral Distribution of Large Random Matrices with i.i.d. Entries." In Random Matrices and Their Applications. Providence, RI: Amer. Math. Soc., pp. 145-152, 1986)

Complex Multiplication (special meaning for elliptic curves?)

Condensation (Macmillan, R. H. A New Method for the Numerical Evaluation of Determinants." J. Roy. Aeronaut. Soc. 59, 772, 1955.)

Cone Net (Nowakowski, M. Matematyka, No. 1 (29), 1954.)

Confluent Hypergeometric Differential Equation (Previato: discuss links with differential equations, geometry, and 19th century mathematics. A suggestion of where hypergeometric functions arise, a glimpse of Riemann surfaces?)

Confluent Hypergeometric Function of the First Kind (Previato: discuss links with differential equations, geometry, and 19th century mathematics. A suggestion of where hypergeometric functions arise, a glimpse of Riemann surfaces?)

Confluent Hypergeometric Function of the Second Kind (Previato: discuss links with differential equations, geometry, and 19th century mathematics. A suggestion of where hypergeometric functions arise, a glimpse of Riemann surfaces?)

Conformal Projection (Germain 1865)

Congruence (Schroeppel: for prime moduli, sqrt a = +- sqrt b, and kth roots work when k is relatively prime to p-1.)

Conic Section (Chasles, M. Traité des sections coniques. Paris, 1865.)

Connex (Clebsch, A. "Ueber ein neues Grundgebilde der analytischen Geometri der Ebene." Göttinger Nachr. No. 22, 1872. Reprinted in Math. Ann. 6, 203-225, 1873.; Godt. Ueber den Connex ester Ordnung und zweiter Classe. Göttingen, Germany, 1873.; Hirst. Proc. London Math. Soc. 63, 1874; Sintsof. Theory of the Connex in Space, in Connection with the Theory of Partial Differential Equations of the First Order. Publications of Kasan University, 1895.; Sintsof. "Theorie des connexes dans l'espace." Bull. des Sci. Math., p. 176, 1898. Stephanos. Bull. Sci. Math. 4, 1880.;)

Continued Fraction (Wallis, J. Arithmetica Infinitorum. Oxford, England, 1656. [Various sources list the publication date as 1653, 1655, and 1656. Which is correct?])

Contractible (add Margherita's images contractible1.bmp, etc.)

Convex Polyhedron (Proc. CUPM Geometry Conf. Math. Assoc. Amer, No. 16, p. 21, 1967)

Correlation Dimension (fractal Whitney embedding prevalence theorem)

Costas Array (Beard, J. K.; Russo, J. C.; Erickson, K.; Moneleone, M.; and Wright, M. "Combinatoric Collaboration on Costas Arrays and Radar Applications." In Proceedings of the IEEE 2004 Radar Conference, April 26-29 2004. [EDITORS? CITY? PUBLISHER?] pp. 260-265, 2004.; Rickard, S.; Connell, E.; Duignan, F.; Ladendorf, B.; Wade, A. "The Enumeration of Costas Arrays of Size 26." In 2006 40th Annual Conference on Information Sciences and Systems. Princeton, NJ: pp. 815-817, 2006. [PUBLISHER?])

Cosymmedian Triangles (figure)

Cousin Primes (sloane: 1.1970449)

Cover (define "covers")

Császár Polyhedron (can't render properly in LiveGraphics3D)

Cubic Number (Moret Blanc 1879; Sphinx. pp. 72 and 87 1937.;)

Cubic Symmetric Graph (sloane: 0, 0, 0, 1, [cubic symmetric graphs on 2n nodes; need more terms])

Cyclidic Coordinates (Darboux, G. "Sur l'application des méthodes de la physique mathématique à l'étude de corps terminés par des cyclides." Comptes Rendus Acad. Sci. Paris 83, 1099, 1864. Wangerin. Preisschriften der Jablanowski'schen Gesellschaft, No. 18, 1875-1876. Wangerin. Crelle's J. 82, 1875-1876. Wangerin. Berliner Monatsber. 1878.)

Daisy (Previato: Is there a place where the mathematical formulas for how many blobs one gets for given prescription (equation of the spiral, which can be algebraic or transcendental, radius of the blobs etc.)?)

de Moivre-Laplace Theorem (de Moivre, A. Miscellanea analytica. Lib. 5, 1730.)

de Polignac's Conjecture (de Polignac, A. Comptes Rendus Paris 29, 400 and 738-739, 1849.)

Difference of Successes (check formulas; find reference)

Differentiable (Hermite 1893)

Diophantine Equation--3rd Powers (Euler, L. Novi. Comm. Acad. Petrop. 6 (ad annos 1756-1757), p. 181, 1761. Euler, L. Comm. Arith. Coll. 1, 207, 1849.)

Diophantine Equation--4th Powers (Martin 1910; Baudran 1885; Euler, L. Nova Acta Acad. Petrop. as annos 1795-1796 13, 45, 1802.; Fauquembergue, E. L'intermédiaire des Math. 5, 33, 1898.; Ferrari, F. L'intermédiaire des Math. 20, 105-106, 1913.; Gérardin, A. Assoc. Franc. 39, 236, 1911. [GARBLED CITATION?]; Gérardin, A. Bull. Soc. Philomathique 3, 236, 1911. [WRONG VOLUME]; Werebrusow, A. L'intermédiaire Math. 20, 105-106, 1913. [NO SUCH AUTHOR OR ARTICLE WITH THIS CITATION])

Diophantine Equation--5th Powers (LEO can't find as cited; will provide ILL microfilm: Martin, A. Smithsonian Misc. Coll. 33, 1888.)

Diophantine Equation--8th Powers (Find original citation; Letac, A. Gazetta Mathematica 48, 68-69, 1942)

Disk Line Picking (Pure, R.; Durran, S.; Tong, F.; Pan, J. "Distance Distribution Between Two Random Points in Arbitrary Polygons." To appear in Math. Meth. Appl. Sci.)

Disk Triangle Picking (VERIFY CITATION: Woolhouse, W. S. B. "Some Additional Observations on the Four-Point Problem." Mathematical Questions, with Their Solutions, from the Educational Times, Vol. 7. London: F. Hodgson and Son, p. 81, 1867.)

Divisor (Chalde [INITIALS?] [TITLE?] Nouv. Ann. Math. 3, 471-473, 1903.; Minin, A. P. [TITLE?] Math. Soc. Moscow 11, 632, 1883-84.; Fontené, G. [TITLE?] Nouv. Ann. Math. 2, 288, 1902.)

Dixon's Factorization Method (provide concrete example)

Donkin's Theorem (add figure)

Double-Free Set (hyphen to dash)

Doubly Periodic Function (Jacobi, C. G. J. J. für Math. 13, 55-56, 1835. Reprinted in Gesammelte Werke, Band II. pp. 25-26, 1882.)

Dowker Notation (gopher://math.berkeley.edu:70/11/Topology/VFRJones/f3to10)

Ear (add figure)

Edgeworth Series (Cramér, H. "On Some Classes of Series Used in Mathematical Statistics." Proceedings of the Sixth Scandinavian Congress of Mathematicians, Copenhagen. pp. 399-425, 1925.)

Eisenstein Integer (Bachmann, P. Allgemeine Arithmetik der Zahlkörper. [CITY, PUBLISHER?] p. 142. [YEAR?])

Eisenstein Series (reference for (2), which seems to require dependence on a and b)

Elements (how to make italic bold+italic)

Ellipsoid Geodesic (Dragovich, V. J. Phys. A 29, L317, 1996. Dragović, V. math-ph/0008009 (2000). Knörrer, H. Invent. Math. 59, 119, 1980. Kravchenko, N. N. Vestnik Mosk. Univ Ser. 1, No. 4, 69, 1996. Tabanov, M. B. Russian Acad. Sci. Dokl. Math. 48, 438, 1994. Toth, J. A. Ann. Phys. 130, 1, 1995. Viesel, H. Archiv Math. 22, 106, 1971. Wiersig, J. and Richter, P. H. Z. Naturf. 51a, 219, 1996.)

Elongated Dodecahedron (Tutton. Crystallography and Practical Crystal Measurement. London, pp. 567 (Fig. 448) and 723 (Fig. 585), 1922. Fedorov. "Elemente der Gestaltenlehre." Mineralogicheskoe obshchestvo Leningrad (Verhandlungen der Russisch-Kaiserlichen Mineralogischen Gesellschaft zu St. Petersburg 21, 1-279, 1885.)

Elongated Square Gyrobicupola (Miller, J. C. P. "Polyhedron." Encyclopædia Britannica, 11th ed.)

Engel Expansion (Engel, F. "Entwicklung der Zahlen nach Stammbruechen." Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg. [VOLUME?], pp. 190-191, 1913.)

Enriques Surface (REQ-102006 ILL REPORTS NOT IN TABLE OF CONTENTS: Enriques, F. "Sulla classificazione." Atti Accad. Naz. Lincei 5, 1914.)

Envelope Theorem (Darboux and Zermelo in 1894; Kneser in 1898)

Equal Parallelians Point (ETC: (ab+ac-bc)(3a^2b^2-2a^2bc-6ab^2c+3a^2c^2-4abc^2+b^2c^2)/a)

Euler Formula (geometric interpretation of complex numbers proof from Conway and Guy;)

Euler's Graeco-Roman Squares Conjecture (Jahrb. Math. 48, 71, 1921.; Jahrb. Math. 49, 41-42, 1923. Bose, Shrikhande, and Parker 1959)

Euler's Homogeneous Function Theorem (Euler, L. Nova Acta Acad. Petropol. 7, p. 58, 1778.)

Euler-Lagrange Differential Equation (By dimensional analysis, (27) should be v/z instead of 1/(vz). So I'm guessing something is wrong with (24)-(26))

Euler-Mascheroni Constant (Odena 1982-1983;)

Euler-Mascheroni Constant Approximations (Odena 1982-1983)

Euler Product (Euler, L. "Variae observationes circa series infinitas." St. Petersburg Acad. [VOLUME, PAGES?], 1737.)

Euler's Sum of Powers Conjecture (Letac, A. Gazetta Mathematica 48, 68-69, 1942.)

Exterior Angle Theorem (check Dunham p. 41)

Faà di Bruno's Formula (Dederick, Wall initials;)

Fagnano's Point (figure)

Feigenbaum Constant (sloane: accurate values for Gamma=2.637?;)

Fermat's Last Theorem (Genocchi 1852; Mirimanoff 1905; Lebesgue 1840; Vandiver 1914; Vandiver, H. S. Fermat's Last Theorem and Related Topics in Number Theory. Ann Arbor, MI [PUBLISHER?]: 1935; L'Intermédiaire des Math. 15, 217-218.; Swinnerton-Dwyer, P. Nature 364, 13-14, 1993)

Fermat Number (Fermat 1650; Eisenberg 1844; Keller, W. "Factors of Fermat Numbers and Large Primes of the Form k·2^n+1, II." In prep.)

Fermat Prime (Eisenstein 1844)

Feuerbach Hyperbola (Mandart H. "Sur l'hyperbole de Feuerbach." Mathesis [VOLUME?], 81-89, 1893.)

Fibonacci Number (Hoggatt III+IV)

First Lemoine Circle (Lemoine. Assoc. Français pour l'avancement des Sci. 1873.)

Folding ([AUTHOR?]. "National Standards and Emblems." Harper's New Monthly Magazine 47, No. 278, 171-181, July 1873.;)

Four Travelers Problem (figure)

Frenet Formulas (figure)

Fresnel's Elasticity Surface (Christoffel, E. B. [TITLE?] Ann. di Mat. (Ser. 2), t. 8, [VOLUME? PAGES?], 1877.)

Fuhrmann's Theorem (displace b'; Fuhrmann reference)

Gauss's Circle Problem (Sierpinski 1906; van der Corput 1923)

Gauss's Interpolation Formula (Abramowitz and Stegun don't show if it is plus or times 2 terms)

Gauss-Jackson Method (Cowell, P. H. [TITLE?] Appendix to Greenwich Observations. [CITY?], England: Bellevue, [PAGES?], 1909.)

Gauss-Kronrod Quadrature (Kronrod, A. S. [Russian]. Doklady Akad. Nauk SSSR 154, 283-286, 1964. Patterson, T. N. L. Math. Comput. 22, 847-856 and C1-C11, 1968. Patterson, T. N. L. Math. Comput. 23, 892, 1969.)

Gauss's Theorema Egregium (is syntax -R(v,w)v,w correct?)

Generalized Moore Graph (McKay, B. D. and Stanton, R. G. "The Current Status of the Generalised Moore Graph Problem." In Combinatorial Mathematics VI (Armidale 1978). New York: Springer-Verlag, pp. 21-31, 1979.)

Geometric Construction (Adler, A. Theorie der geometrischen Konstruktionen.; Enriques, F. Fragen der Elementargeometrie, Vol. 2.; Vahlen, K. T. Konstruktionen und Approximation.)

Geometric Homology (Lambert, J. H. Freie Perspective, 2nd ed. Zürich, 1774.)

Girard's Spherical Excess Formula (Girard, A. Invention nouvelle en algebra. Amsterdam, Netherlands, 1629.)

Giuga Number (Kellner, B. C. "The Equivalence of Giuga's and Agoh's Conjectures." Preprint. 10 July 2003.)

Glaisher-Kinkelin Constant (Glaisher 1877)

Global C(G;T) Theorem (make title bold italic)

Goldbach Conjecture (Desboves, A. Nouv. Ann. Math. 14, 293, 1855. [can't find as cited]; Borodzkin 1956 (16.038?); Schnirelman, L. G. Uspekhi Math. Nauk 6, 3-8, 1939.;)

Golygon (Gardner)

Gompertz Constant (Stieltjes)

Greatest Common Divisor (string figure; Knuth ref)

Green's Function--Poisson's Equation (check derivation in arfken)

Gröbner Basis (Stoutemyer, D. "Which Polynomial Representation is Best? Surprises Abound!" In Proceedings of the Third MACSYMA Users' Conference, Schenectady, NY. pp. 221-243, 1984.)

Grundy's Game (line break)

Hammer's X-Ray Problems (Croft references)

Hard Hexagon Entropy Constant (Katzenelson, J. and Kurshan, R. P. "S/R: A Language for Specifying Protocols and Other Coordinating Processes." In Proc. IEEE Conf. Comput. Comm., pp. 286-292, 1986.)

Hardy-Littlewood Tauberian Theorem (Hardy, G. H. and Littlewood, J. E. Quart. J. Math. 46, 215-219, 1915. Hardy, G. H. and Littlewood, J. E. Acta Math. 41, 119-196, 1918.; Karamata. Math. Z. 32, 319-320, 1930.)

Harmonic Mean Index (why is p_0q_0 summed over? Seems strange, but Kenney and Keeping do it)

Harmonic Series (more terms of 2.163)

Hart's Inversor (Mannheim, A. "Sur l'inverseur de Hart." Messenger Math. [VOLUME?], p. 151 [ENDING PAGE?], Nov. 1896)

Hartley Transform (modify discrete case to use plus sign convention)

Hausdorff Paradox (add some references; this entry is too vague; no references in Le Lionnais)

Heart Curve (sloane: 3.661972725)

Helson-Szegö Measure (what is bar y?)

Hempel's Paradox (details; Hempel, C. G. "A Note on the Paradoxes of Confirmation." Mind 55, 1946)

Heptagonal Triangle (Bankoff, L. and Garfunkel, J. "Problem E1222." Amer. Math. Monthly [VOLUME?], 110-112, Feb. 1957. Bankoff, L. and Garfunkel, J. "Problem E681." Amer. Math. Monthly [VOLUME?], 219, Sep. 1968. Bankoff, L. and Garfunkel, J. "Problem 189." Pi Mu Epsilon J. [VOLUME, PAGES?], Spring 1968.)

Hering Illusion (Hering, Ewald (1861))

Hessian Covariant (describe symbols)

Hexyl Triangle (ETC: 3a^3-ba^2-ca^2-3b^2a-3c^2a+2bca+b^3+c^3-bc^2-b^2c)

Hilbert's Axioms (add: actually include all 21 explicitly; http://www.math.uncc.edu/ droyster/math3181/notes/hyprgeom/node27.html http://www.math.uncc.edu/ droyster/courses/spring02/classnotes/Chapter02.pdf)

Hirota Equation (should abs(u squared) be (abs u)squared?)

Hoffman's Minimal Surface (figure)

Hofstadter Ellipse (ETC: center; ETC: fourth intersection with circumcircle)

Hofstadter Triangle (figure)

Hölder's Inequalities (Hölder, O. "Über einen Mittelwertsatz." Göttingen Nachr., 44, 1889.)

Hypergeometric Function (Thomae [INITIAL?]. [TITLE?] J. reine angew. Math. 87, 222-349, 1879.)

Hyperreal Number (Robert Goldblatt, R.; Axler, S.; Gehring, F. W.; Halmos, P. R. Lectures on the Hyperreals: An Introduction to Nonstandard Analysis. New York: Springer-Verlag)

Hypersphere Packing (Lagrange, J.-L. "Recherches d'arithmétique." Nouv. Mém. Acad. Roy. Soc. Belles Lettres (Berlin), [VOLUME?] pp. 265-312, 1773. Reprinted in Oeuvres, Vol. 3, pp. 693-758. [CITY, PUBLISHER, YEAR?])

i (Asimov, I. "The Imaginary." Super Science Stories. [VOLUME/ISSUE, PAGES?] Nov. 1942.)

I (Horvat, B.; Pisanski, T.; and Žitnik, A. "Isomorphism Checking of I-Graphs." Submitted.; Petkovšek, M. and Zakrajšek, H. "Enumeration of I-Graphs: Burnside Does It Again." To appear in Ars Math. Contemp. 3, 2010.;)

Icosahedral Equation (Klein, F. "Sull' equazione dell' Icosaedro nella risoluzione delle equazioni del quinto grado [per funzioni ellittiche]." Reale Istituto Lombardo, Rendiconto, Ser. 2 10, 1877)

Icosian Game (Hamilton, W. R. [TITLE?] Quart. J. Math., 5, 305 [PAGE RANGE?], 1862. Hamilton, W. R. [TITLE?] Philos. Mag. 17, 42 [PAGE RANGE?], 1884.)

Ideal (David Vanvactor recommends adding a discussion of representation and multiplication of ideals)

Idempotent Number (add references listed in Sloane sequences)

Imaginary Number (Asimov, I. "The Imaginary." Super Science Stories. [VOLUME/ISSUE, PAGES?] Nov. 1942.)

In-and-Out Curve (reference)

Incircle (analytically compute Well's theorem)

Inclusion-Exclusion Principle (da Silva. "Proprietades geraes." J. de l'Ecole Polytechnique, cah. 30.)

Independent Set (Hochbaum, D. S. (Ed.). Approximation Algorithms for NP-Hard Problems. [CITY?] PWS Publishing, 1997)

Information Dimension (Balatoni, J. and Renyi, A. Pub. Math. Inst. Hungarian Acad. Sci. 1, 9, 1956.)

Invariable Point (figure)

Inversion (Thomson, W. "Extrait de deux lettres adressées à M. Liouville." J. math. pures appl. 12, 256, 1847.)

Isoclinic Groups (truncated last sentence?)

Isogonal Line (Label figure)

Isolated Singularity (check table)

Isomorphic Factorization (Exoo 2005; Royle 2004)

Isosceles Tetrahedron (Chefik-Bey. Nouv. Ann. 19, 403, 1880. Monge, G. Corresp. sur l'École Polytech., pp. 1-6, 1809. Jacobi, C. F. A. In Swinden, J. H. Elemente. p. 457, 1834. Lemoine, E. Z. Math. u. Physik 29, 321, 1884. Biddle, D. Mathesis, p. 91, 1931)

Jacobi Amplitude (Jacobi, C. G. J. [TITLE] J. für Math. 18, 12 and 20, 1838.)

Jacobi's Imaginary Transformation (Poisson, S. Mém. de l'Acad. des Sci. 6, 592, 1827.)

Johnson's Theorem (Mackenzie, D. "Triquetras and Porisms." College Math. J. [VOLUME?] pp. 118-131. March 1992.)

Jonquière's Theorem (Jonquière, A. "Mémoire sue les contacts multiples d'ordre quelconque de courbes, etc. [REST OF TITLE?]" J. reine angew. Math. 66, 288 [END PAGE?], 1866; Zeuthen [INITIAL?]. Lehrbuch der abzählenden Methoden in der Geometrie. Leipzig [PUBLISHER?], p. 240 [ENDING PAGE?], 1914.)

Jordan Decomposition Theorem (what does A have to do with anything)

Josephus Problem (Bachet, C. G. Problem 23 in Problèmes plaisans et délectables, 2nd ed. [CITY, PUBLISHER], p. 174, 1624.)

Joyce Sequence (Laisant, C. A. 1906; Uhler 1947)

Julia Set (Douady;)

Karatsuba Multiplication (Bernstein, D. J. "Fast Multiplication and Its Applications." To appear in Alg. Number Th.)

Keith Number (sloane: 71 and 1593583.)

Keller Graph (Jarnicki et al. 2017. Preprint)

Kelvin's Conjecture (Matzke, E. Amer. J. Botany 32, 130, 1946.; Princen, H. M. and Levinson, P. J. Colloid Interface Sci. 120, 172, 1987.; Ross, S. Amer. J. Phys. 46, 513, 1978.; Thomson, W. Philos. Mag. 25, 503, 1887.; Weaire, D. Philos. Mag. Let. 69, 99, 1994.; Williams, R. Science 161, 276, 1968.)

Kieroid (plot)

Kirkman Points (Hesse, O. Vorlesungen über analytische Geometrie des Raumes. Leipzig [PUBLISHER]?, p. 186, 1861 [IS THIS THE RIGHT REFERENCE?]; Kirkman, T. P. [TITLE?] Cambridge Dublin Math. J. 5, 185. [ENDING PAGE?] [YEAR?])

Kirkman's Schoolgirl Problem (RARE BOOK: Kirkman, T. P. Lady's and Gentleman's Diary. 1850. Woolhouse. Lady's and Gentleman's Diary. 1862-1863. Carpmael. Proc. London Math. Soc. 12, 148-156, 1881.)

Kleinian Group (add figure)

Knight Graph (Jaenisch. Chess Monthly 1859. Roget, P. M. Philos. Mag. 16, 305-309, 1840. Warnsdorff, H. C. Des Roesselsprungs einfachste und allgemeinste Loesung. Schmalkalden, 1823.)

Knot (ftp://chs.cusd.claremont.edu/pub/knot; Schubert, H. Sitzungsber. Heidelberger Akad. Wiss., Math.-Naturwiss. Klasse, 3rd Abhandlung. 1949; Przytycki, J. "A History of Knot Theory from Vandermonde to Jones." Proc. Mexican Nat. Congress Math., Nov. 1991.)

Kobon Triangle (Do these appear in Kobon Fujimura's The Tokyo Puzzles. Frederick Muller Limited, 1981 New York, Charles Scribner's 1978 (?) (Gardner does not say.))

Kolakoski Sequence (Sellke [FIRST INITIAL?]. Problem 324 in Statistica Neerlandica 50, 222-223, 1996.)

Kollros' Theorem (Kollros 1938)

Lagrange Bracket (Lagrange. Mém. de l'Institute de France, 1808. Reprinted in Oeuvres, Vol. 4. p. 713)

Lagrange Interpolating Polynomial (Pearson, K. [TITLE?] Tracts for Computers 2, [PAGES?] 1920.; Waring, E. [TITLE?] Philos. Trans. 69, 59-67, 1779.)

Lanczos Approximation (Lanczos, C. [TITLE?] J. Soc. Indust. Appl. Math. Ser. B: Numer. Anal. 1, 86-96, 1964.)

Landau-Ramanujan Constant (Gosper formula doesn't seem to quite hold)

Landau Symbols (Bachmann, P. Analytische Zahlentheorie. 1894. Landau, E. 1909)

Laplace's Equation (Moon, P. and Spencer, D. E. "Recent Investigations of the Separation of Laplace's Equation." Proc. Amer. Math. Soc. 4, 302 [ENDING PAGE?], 1953.)

Lattice Sum (add definition)

Leading Order Analysis (define psi function)

Least Squares Fitting (Gauss, C. F. "Theoria combinationis obsevationum erroribus minimis obnoxiae." Werke, Bd. 4. Göttingen, [PUBLISHER?] p. 1 [PAGE RANGE], 1823.;)

Leg (figure)

Legendre's Chi-Function (Legendre, A. M. Exercices de calcul intégral, tome 1. p. 247, 1811.)

Lemoine Cubic (Lemoine, E. [TITLE?] Association Française pour l'Avancement des Sciences. [VOLUME?] p. 149 [PAGE RANGE?], 1891.; Lemoine, E. [TITLE?] Association Française pour l'Avancement des Sciences. [TITLE?] p. 124 [PAGE RANGE?], 1892.;)

Liar's Paradox (Fraenkel, A. A. and Bar-Hillel, Y. Foundations of Set Theory. Amsterdam, Netherlands, p. 11, 1958.; Weyl, H. Philosophy of Mathematics and Natural Science. Princeton, NJ, p. 228, 1949)

Linkage (Kempe, A. B. How to Draw a Straight Line: A Lecture on Linkages. 1977.)

Lion and Man Problem (Rado, P. A. and Rado, R. [TITLE?] Math. Spectrum 7, 89-93, 1974/75.)

Littlewood-Salem-Izumi Constant (Arias de Reyna, J. and van De Lune, J. "High Precision Computation of a Constant in the Theory of Trigonometric Series." Math. Comput. Published electronically, February 9, 2009.)

Local Density (reference. Stewart?)

Logarithmic Integral (Soldner. [TITLE?] Abhandlungen 2, 333 [ENDING PAGE?], 1812.)

Logarithmic Spiral Catacaustic (find exact relation between original and catacaustic)

Logistic Map (Andrecut 1998; Gonzáles and Pino 1999, 2000; Gonzáles et al. 2001ab; Umeno 1998; Wong et al. 2001;)

Lommel Function (Lommel, E. C. J. von. "Die Beugungserscheinungen einer kreisrunden Oeffnung und eines kreisrunden Schirmchens theoretisch und experimentell bearbeitet." Abh. der math. phys. Classe der k. b. Akad. der Wiss. (München) 15, 229-328, 1886.: page range listed as 229-328 and 233-328 on pp. 537 and 772 of Watson, resp.; Lommel, E. C. J. von. "Die Beugungserscheinungen geradlinig begrenzter Schirme." Abh. der math. phys. Classe der k. b. Akad. der Wiss. (München) 15, 531-663, 1884-1886.: page range listed as 529-664 and 531-663 on pp. 537 and 772 of Watson, resp.;)

Longimeter (Steinhaus, H. Mitteilungen der Sächsischen Akad. 82, 120-130, 1930.; Steinhaus, H. Przeglad Geogr. 21, 1947.; Steinhaus, H. Comptes Rendus Soc. des Sciences et des Lettres de Wrocław, Sér. B, 1949.)

Longuet-Higgins Circle (Woo, P. Y. "Solution of Problem 10734." Amer. Math. Monthly [VOLUME? PAGES? YEAR?])

Longuet-Higgins Point (Woo, P. Y. "Solution of Problem 10734." Amer. Math. Monthly [VOLUME? PAGES? YEAR?])

Lost in a Forest Problem (Bellman, R. "Minimization Problem." Bull. Amer. Math. Soc. 62, 270, 1956.; Berzsenyi, G. "Lost in a Forest (A Problem Area Initiated by the Late Richard E. Bellman)." Quantum [VOLUME?], p. 41, Nov./Dec. 1995.)

Löwenheim-Skolem Theorem (Skolem, T. "Sur la portée du théorème de Löwenheim-Skolem." Les Entretiens de Zurich sur les fondements et la méthode des sciences mathématiques (December 6-9, 1938), pp. 25-52, 1941. Quine, W. V. Methods of Logic, rev. ed. New York: pp. 253-260, 1959.)

Lubbock's Formula (Lubbock, J. W. Cambridge Philos. Trans. 3, 323, 1829.)

Lyapunov Function (verify definitions involving positive and negative definiteness)

MacBeath Circle (ETC: X933^'=((b-c)^2*(b+c)^2*(a^8-2*a^6*b^2+2*a^2*b^6-b^8-2*a^6*c^2+a^4*b^2*c^2+b^6*c^2+2*a^2*c^6+b^2*c^6-c^8)*Cos[A]*Cos[B-C])/a)

MacBeath Inconic (Serret, P. [TITLE?] Nouv. Ann. Math. [VOLUME?], p. 428 [PAGE RANGE?], 1865.)

Maclaurin Series (sloane: add OEIS numbers)

Magic Tesseract (Trenkler, M. "Magic p-Dimensional Cubes." Submitted to Acta Arith., 2000.; reconcile existence of order 5 magic tesseract)

Magic Tour (Beverly, W. Philos. Mag. p. 102, Apr. 1848.; Murray, H. J. R. The Magic Knight's Tours, a Mathematical Recreation. [PUBLISHER, CITY?] 1951.; Wenzelides, C. Schachzeitung, p. 247, 1849.)

Malfatti's Problem (Hart, [INITIAL?]. [TITLE?] Quart. J. 1, p. 219. [YEAR?]; Oswald, [INITIAL?]. [TITLE?] Klassiker de exakten Wissenschaften, Vol. 23. Suppl. [PAGES?] [YEAR?]; Schellbach, [INITIAL?]. [TITLE?] J. reine angew. Math. 45 [PAGES?] [YEAR?].)

Mandart Inellipse (Mandart H. "Sur l'hyperbole de Feuerbach." Mathesis [VOLUME?], 81-89, 1893.; Mandart, H. "Sur une ellipse associée au triangle." Mathesis [VOLUME?], 241-245, 1894; find area and axes)

Mandelbrot Set (Mandelbrot; Douady, A. "Julia Sets and the Mandelbrot Set." In The Beauty of Fractals: Images of Complex Dynamical Systems (Ed. H.-O. Peitgen and D. H. Richter). Berlin: Springer-Verlag, pp. 161-?.; Fisher, Y. and Hill, J. "Bounding the Area of the Mandelbrot Set." Submitted to Numer. Math.; Hill, J. R. "Area of Mandelbrot Set Components and Clusters.")

Mannheim's Theorem (figure; Mannheim, A. J. de math. élémentaires, p. 225, 1895.)

Marion's Theorem (Mathematics Teacher. p. 619, Nov. 1993.)

Markov Chain (Discuss transition probabilities)

Mascheroni Construction (Mascheroni, L. Geometry of Compass. 1797)

Masser-Gramain Constant (check sign of inequality at http://euklid.mi.uni-koeln.de/ mwelter/Ganzwertig/Ganzwertig.html)

Matrix (Sylvester, J. J. "Additions to the Articles 'On a New Class of Theorems' and 'On Pascal's Theorem.' " Philos. Mag. [VOLUME?], 363-370, 1850.)

Medial Triangle (Carding, M. "Culture Shock for Mathematics and Science." Math. Today 42, [PAGES?] Aug. 2006)

Meijer G-Function (Meijer, C. S. Nieuw Arch. Wisk. 18, 10-39, 1936. [BAD REF])

Meixner Polynomial of the Second Kind (discrepancy between Roman and me for G.F.)

Mellin-Barnes Integral (Pincherle, S. Atti d. R. Academia dei Lincei, Ser. 4, Rendiconti 4, 694-700 and 792-799, 1888)

Menelaus' Theorem (check)

Mersenne Prime (According to Schroeppel, a British guy "Hayworth, Guy" has a nice memo about discovery and proofs of Mersenne numbers; Miller, J. C. P. and Wheeler, D. J. Nature 168, 838, 1951; Uhler, H. S. Scripta Math. 18, 122-131, 1952.; Mersenne, M. Cogitata Physico-Mathematica. 1644. Cole. 1903. Landry. 1869. Lehmer. 1947. Penk and Baillie. 1979. Poulet. 1923 Sandia 1984 Pomerance and Wagstaff Sci News Cataldi. Euler. 1750. Lehmer. 1952-3. Lucas. 1876. Pervouchine. 1883. Seelhoff. 1886. Slowinski, D. Jan. 29, 1988. Slowinski, D. Sci. News 139, 191, 9/16/1989)

Mertens Conjecture (Stieltjes, T. [TITLE?] C. R. A. S. [VOLUME?], [PAGE RANGE?], 1885.)

Mertens Constant (Mertens, F. J. für Math. 78, 46-62, 1874.)

Mertens Function (add sloane sequences from table)

Mice Problem (Clapham, A. J. [TITLE?] Rec. Math. Mag., [VOLUME, PAGES?] Aug. 1962.; Marshall, J. A.; Broucke, M. E.; and Francis, B. A. "Pursuit Formations of Unicycles." Automata 41, [PAGES?] 2005.)

Minimal Enclosing Circle (Chrystal [INITIALS?]. "On the Problem to Construct the Minimum Circle Enclosing n Given Points in a Plane." Proc. Edinburgh Math. Soc. [VOLUME?], Third Meeting, p. 30 [ENDING PAGE?] Jan 9, 1885.)

Minimal Surface (Lagrange. "Essai d'une nouvelle méthode pour déterminer les maxima et les minima des formules intégrales indéfinies." 1776; Radó, T. "On the Problem of Plateau." Ergeben. d. Math. u. ihrer Grenzgebiete. Berlin: Springer-Verlag, 1933.;)

Minkowski Convex Body Theorem (Warmus, W. Colloq. Math. I 1, 45-46, 1947.)

Miquel's Theorem (Kimberling, C. "Transfigured Triangle Geometry." Preprint. Mar. 5, 2005.)

Möbius Function (Landau, E. Wiener Sitzungsber. 120, 973-988, 1911.; Landau, E. Prac. Matematyczno-Fizycznych 21, 97-177, 1910.)

Möbius Strip (Listing and Tait. Vorstudien zur Topologie, Göttinger Studien, Pt. 10, 1847.; Möbius, A. F. Werke, Vol. 2. p. 519, 1858.)

Mock Theta Function (Bellman (1961, p. 51), the first term in the Denominator is (erroneously?) written (1+q)^2)

Moduli Space (Kirwan, F. "Introduction to Moduli Spaces." In Proceedings of the EWM Workshop on Moduli Spaces, Oxford, EWM. 1999.)

Moiré Pattern ([AUTHOR?] Moire Patterns Draw Contours, and a Meter Determines Current in Electrostatic Circuits. Sci. Amer. [VOL?] [PAGES?], October, 1973.; THIS REFERENCE APPEARS TO BE WRONG: Gardner, M. The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, pp. 229-230, 1984.)

Monge Point (figure; Monge, G. Corresp. sur l'École Polytech. 2, 266, 1795.)

Monge's Tetrahedron Theorem (figure; Forder, H. G. Math. Gaz. 15, p. 470, 1930-1931. Monge, G. Corresp. sur l'École Polytech. 2, 266, 1795.)

Moore Graph (sloane: 0,0,0,1,1,2,1,2,1,3,1,2,1, ...[too many sequences match the initial nonzero terms])

Morse Theory (Rassias, G. (Ed.). Morse Theory and Its Applications.)

Moses-Longuet-Higgins Circle (ETC: (a^2(S_A-4s_a^2)+4(s_c^2S_B+s_b^2S_C))/a)

Mott Polynomial (inconsistency in Roman)

Multiperfect Number (Carmichael and Mason, T. E. Proc. Indian Acad. Sci., 257-270, 1911)

Mycielski Graph (Jarnicki et al. 2017)

Napoleon's Problem (Mascheroni, L. Geometria del compasso. 1797. Schwerin. Mascheronische Konstruktionen. 1898.)

Narcissistic Number (Rumney, M. [AUTHOR CORRECT?] "Digital Invariants." Recr. Math. Mag. No. 12, 6-8, Dec. 1962)

Nelder-Mead Method (Wright, M. H. "The Nelder-Mead Method: Numerical Experimentation and Algorithmic Improvements." AT&T Bell Laboratories Techn. Rep. Murray Hill, NJ.)

Nested Radical (Ramanujan, S. Question No. 298. J. Indian Math. Soc. [VOLUME, PAGES?] 1911.)

Newton-Cotes Formulas (Daniell, P. J. "Remainders in Interpolation and Quadrature Formulae." Math. Gaz. 24, 238, 1940.)

Nine-Point Circle (Lange, J. Geschichte des Feuerbach'schen Kreises. Berlin, 1894.)

Niven's Constant (limit of Zeta[3/2]/Zeta[3] doesn't seem to be right)

Noncentral F-Distribution (Bulgren, W. G. "On Representations of the Doubly Non-Central F Distribution." J. Amer. Stat. Assoc. 66, 184, 1971)

Number (Frege. Grundgesetze der Arithmetik.)

Nyquist Frequency (Arndt, J. Algorithms for Programmers: Ideas and Source Code. In preparation.)

Ochoa Curve (ILL: not found as cited: Crux 1987 248; ILL not found as cited: Crux 1989 41; Ochoa Melida, J. "La ecuacion diofántica b_0y^3-b_1y^2+b_2y-b_3=z^2." Gaceta Math. 139-141, 1978.)

Odd Part ("Problem H-81." Fib. Quart. 6, 52, 1968.)

Odd Sequence (missing definition)

Operations Research (INFORMS. Operations Research: 50th Anniversary Issue. Linthicum, MD, 2002.)

Orbifold (Previato: add references)

Orchard-Planting Problem (Educ. Times Reprints 8, 106, 1868. Educ. Times Reprints 45, 127-128, 1886.)

Orthocentric System (add labels)

Orthopolar Line (Servais, Cl. "Sur l'orthopóle." Mathesis, p. 11, 1923.)

Ouchi Illusion (Ashida, H. "Spatial Frequency Tuning of the Ouchi Illusion and Its Dependence on Stimulus Size." To appear in Vision Research.)

Oval (Dixon, R. "The Drawing Out of an Egg." New Sci., July 29, 1982.)

Pancake Sorting (Morales L. and Sudborough, I. H. "A Quadratic Lower Bound for Reverse Card Shuffle." Presented at 26th S.E. Conf. Comb. Graph Th. Computing. Preprint 1995. [PROC. TITLE, EDITORS, PUBLISHER, PAGES, YEAR?])

Pandigital Fraction (Friedman, M. J. Scripta Math. 8.)

Paper Bag Surface (Robin, A. C. [TITLE?] Math. Today. [VOLUME?], 104-107, June 2004.)

Paris-Harrington Theorem (Paris, J. and Harrington, L. "A Mathematical Incompleteness in Peano Arithmetic." In Handbook for Mathematical Logic (Ed. J. Barwise). Amsterdam, Netherlands: North-Holland, [PAGE RANGE?], 1977.)

Partition Function P (Mordell 1922)

Partition Function P Congruences (Dyson, F. J. [TITLE?] Eureka 8, 10-15, 1944.;)

Pascal's Theorem (Cayley, A. Quart J. 9, p. 348.; Leibniz, G. Letter to M. Périer. In Œuvres de B. Pascal, Vol. 5 (Ed. Bossut). p. 459. Veronese. "Nuovi Teremi sull' Hexagrammum Mysticum." Real. Accad. dei Lincei. 1877.)

Pathological (Poincaré 1899)

Pearson System (locate type 8)

Peaucellier Inversor (Sarrus. Comptes Rendus de l'Académie de Paris 36, 1036, 1853.)

Pedal Curve (Ueda, K. In Mathematical Methods for Curves and Surfaces (Ed. T. Lyche and L. L. Shumaker). Nashville, TN: Vanderbilt University Press, [PAGE RANGE?], 2001.)

Pedal Line (figure)

Pell Equation (Nasimoff, P. S. Ch. 1 in Application of Elliptic Functions to the Theory of Numbers. Moscow, 1885. French summary in Ann. sci. de l'École normale supér. 5, 23-31, 1888.; Euler, L. Novi Comm. Acad. Petrop. 18, 218, 1773. Reprinted in Opera Omnia, Vol. 3, p. 310. Euler, L. Comm. Arith. 570. Reprinted in Opera Omnia, Vol. 3, p. 310.)

Pentaflake (Aigner, M.; Pein, J.; and Stechmüller, T. [TITLE?] T. Math. Semesterber. 38, 242 [ENDING PAGE?], 1991.; Zeitler, H. [TITLE?] Math. Semesterber. 49, 185 [ENDING PAGE?], 2002.)

Perfect Number (Sylvester (1887). Catalan (1888). Stuyvaert (1896). (Lucas 1891))

Perfect Square Dissection (Descartes, B. "Division of a Square into Rectangles." Eureka, No. 34, 31-35, 1971. Reichert, H. and Toepken, H. Jahresber. deutschen math. Verein. 50, 1940.; Willcocks, T. H. Fairy Chess Review 7, 1948.;)

Periodogram (Schuster. Terrestrial Magnetism 3, 24, 1898)

Permutation Group (Furst, M.; Hopcroft, J.; and Luks, E. "Polynomial Time Algorithms for Permutation Groups." In Proc. Symp. Foundations Computer Sci. IEEE, pp. 36-41, 1980.)

Perrin Pseudoprime (Malo, E. L'Intermédiare des Math. 7, 312-EOA, 1900)

Perrin Sequence (Malo, E. [TITLE?] L'Intermédiare des Math. 7, 281 and 312 [PAGE PRANGES?] 1900)

Perspective (Lambert, J. H. Freie Perspective, 2nd ed. Zürich, 1774.)

Petersen Graph (B. Horvat, T. Pisanski. Unit distance representations of the Petersen graph in the plane. Ars Combin., (to appear).)

Pi Approximations (Castellanos 1988a or b)

Pi Heptomino (new figure)

Pi Iterations (Pfaff 1800)

Pick's Theorem (Steinhaus, H. "O polu figur płlaskich." Przeglad Mat.-Fiz., 1924.; Haigh, G. "A 'Natural' Approach to Pick's Theorem." Math. Gaz. 64, 173-, 1980.)

Pillai's Theorem (Pillai. J. Indian Math. Soc. 19, 1-11, 1931.)

Plaited Polyhedron (Gorham, J. Plaited Crystal Models. 1888.)

Planar Graph (Meyer, J. "L'épaisseur des graphes completes K_(34) et K_(40)." J. Comp. Th. 9, [PAGES?] 1970 (cited in le Lionnais, p. 56))

Plancherel's Theorem (Plancherel 1910; Rayleigh, J. W. S. "On the Character of Complete Radiation at a Given Temperature." Philos. Mag. 27, [PAGES?], 1889.; Titchmarsh, E. C. "A Contribution to the Theory of Fourier Transforms." Proc. London Math. Soc. 23, 279 [ENDING PAGE?], 1924.)

Plane Division by Circles (Problem Q736. Parabola 24, 22, 1988; Indiana School Mathematics J. 14, No. 4, p. 4, 1979.)

Plane Division by Ellipses ([AUTHOR?] Problem Q607. Parabola 20, 27 [ENDING PAGE?], 1984)

Plane Geometry (Fuhrmann, W. Synthetische Beweise Planimetrische Sätze. Berlin, 1890.)

Plateau's Problem (Radó, T. "On the Problem of Plateau." Ergeben. d. Math. u. ihrer Grenzgebiete. Berlin: Springer-Verlag, 1933.)

Plouffe's Constants (Chowdhury, M. "On Iterates of the Chaotic Logistic Function t_(n+1)=4t_n(1-t_n)." Unpublished note, 2001.; Chowdhury, M. "A Formula for 0.4756260767...." Unpublished note, 2001.)

Plücker Lines (Plücker, M. J. reine angew. Math. 5, p. 274.)

Pohlke's Theorem (Schwarz, H. A. J. reine angew. Math. 63, 309-314, 1864.)

Point-Set Topology (Bing, R. H. "Elementary Point Set Topology." Amer. Math. Monthly 67, No. 7, Aug.-Sep. 1960.)

Poisson Bracket (Poisson. J. de l'École Polytech. 8, p. 266, 1809.)

Poisson Trials (Uspensky)

Poker (Rubens, J. Win at Poker. New York: Dover. [YEAR?])

Pollard rho Factorization Method (Eldershaw, C. and Brent, R. P. "Factorization of Large Integers on Some Vector and Parallel Computers." [JOURNAL, VOLUME, PAGES, YEAR?])

Pólya-Vinogradov Inequality (Vinogradov. [TITLE?] Perm. Univ. Fiz.-Mat. ob.-vo Zh. 1, 18-24 and 94-98, 1918.)

Polyconic Projection (Hunt, [INITIALS?]. Appendix 39 in Report for the U.S. Coast and Geodetic Survey. [CITY, PUBLISHER, PAGES?] 1853.)

Polygon Diagonal Intersection Graph (Meeus, J. [TITLE?] Wiskunde Post (Belgium) 10, 62-63, 1972.)

Polyhe (add figures)

Polyhedral Formula (Euler, L. "Elementa doctrine solidorum." Reprinted in Opera, Vol. 26, pp. 71-92. [PUBLISHER, CITY, YEAR])

Polyiamond (Gardner, M. "Mathematical Games: On Polyiamonds: Shapes That are Made Out of Equilateral Triangles." Sci. Amer. 211 [PAGES?], Dec. 1964)

Polyomino (Applied Combinatorial Mathematics, pp. 201 and 213;)

Poncelet's Porism (Cayley, A. Phil. Mag. 5, 281-284, 1853.; Cayley, A. Phil. Mag. 6, 99-102, 1853.; Cayley, A. Phil. Trans. Roy. Soc. London 151, 225-239, 1861.; Chaundy, T. W. Proc. London Math. Soc. 22, 104-123, 1923.; Chaundy, T. W. Proc. London Math. Soc. 25, 17-44, 1926.; Clifford, W. K. Proc. London Math. Soc. 7, 29-38.; Clifford, W. K. Proc. London Math. Soc. 7, 225-233.; Clifford, W. K. Proc. Cambridge Phil. Soc., 120-123, 1868.; Darboux, G. Comptes Rendus de l'Acadamie de Sciences 90, 1880.; Darboux, G. Principles de géométrie analytique, Vol. 3. Paris, pp. 250-287, 1917.; Davis, M. A. Educ. Times 32.; Durége. Theorie der Elliptischen Functionen. p. 185.; Educ. Times 3, p. 42.; Fuss, N. Nova Acta Petropol. 10, 1792.; Hart. Quart. J. Math., 1857.; Rosanes and Pasch. §9 in J. reine angew. Math. 64, 163-164.; Titchmarsh, E. C. Messenger Math. 52, 42, 1922.; Weill, M. and Bützberger. "Sur les polygones inscrits et circonscrits à la fois à deux cercle." Journal de Liouville, 3me série 4, 7-32, 1878.)

Pong Hau K'i (What does the board actually look like and what in meant by finite graph)

Porism (Playfair, J. [TITLE?] Trans. Roy. Soc. Edinburgh 3, 156 [ENDING PAGE?], 1792.)

Postage Stamp Problem (what does 'local' mean, as in 'local' postage stamp problem?)

Practical Number (A. K. Srinivasen 1948)

Prime Array (Lee, G. Dragon User. May 1984.)

Prime Constellation (sloane: 2.640647264; sloane: 2.858248596; sloane: 4.151180864; sloane: 8.302361728)

Prime Factor (Hardy, G. H. and Ramanujan, S. Quart. J. Math. 48, 76-92, 1917.)

Prime-Generating Polynomial (sloane: -18757, -15619, -12829, -10369, -8221, -6367, -4789, -3469, -2389, -1531, -877; sloane: 50383, 45779, 41381, 37189, 33203,; sloane: 2971, 2477, 2069, 1747, 1511, 1361,; etc.)

Prime Number (references from Hardy and Wright p. 414; Gandhi, J. M. "Formulae for the Nth Prime." Proc. Washington State University Conferences on Number Theory. pp. 96-107, 1971. Guy, R. K. "Divisors and Desires." Amer. Math. Monthly 104, 359-360, 1997.)

Prime Number Theorem (Bochner. Math. Z. 37, 1-9, 1933. Landau, E. Berliner Sitzungsber., 514-521, 1932.; Lu, W. C. "On the Elementary Proof of the Prime Number Theorem with a Remainder Term." Rocky Mountain J. Math. 29, 979, 1999. Vallée Poussin, C. Mém. Couronnés Acad. Roy. Belgique 59, 1-74, 1899.;)

Prime Quadratic Effect (Hardy and Littlewood 1915(?))

Prime Triangle (Kenney, M. J. "Student Math Notes." NCTM News Bulletin. Nov. 1986)

Principle of Insufficient Reason (Keynes, J. M. "Fundamental Ideas." Ch. 4 in A Treatise on Probability. [CITY?] Macmillan, 1921.; Poincaré, H. Ch. 1 in Calcul des probabilités. Paris [PUBLISHER?], 1912. Reprinted [CITY?] Jacque Gabay, 1987.)

Prisoner's Dilemma (check; A Tucker)

Projective Geometry (Chasles, M. Aperçu historique. Chasles, M. Traité de Géométrie supérieure. Paris, 1852. Poncelet, J.-V. Traité des Propriétés Projectives. Paris, 1822. Reye. Geometrie der Lage, 2nd ed. Hannover, Germany, 1877. Steiner, J. Systematische Entwicklung der Abhängigkeit geometrischer Gestalten von einander. Berlin, 1832.)

Prüfer Ring (Fontana, M.; Huckaba, J. A.; and Papick, I. J. Prüfer Domains. New York: Dekker.)

Puiseux's Theorem (Puiseux, V. "Recherches sur les fonctions algébriques." J. de math. pures et appl. 15, 207, 1850.)

Puzzle (references; Clessa, J. J. Math and Logic Puzzles for PC Enthusiasts. New York: Dover. Costello, M. J. The Greatest Puzzles of All Time. New York: Dover.)

Pythagorean Triple (The case a_0=1 is not covered by (24); check Honsberger: Garfunkel, J. Pi Mu Epsilon J. 1981, p. 31.)

Q (Bourbaki, N. Éléments de mathématique: Algèbre. [CITY, PUBLISHER, YEAR, PAGE?])

q-Dimension (Grassberger, P. "Generalized Dimensions of Strange Attractors." Phys. Lett. A 97, 227, 1983. Hentschel, H. G. E. and Procaccia, I. "The Infinite Number of Generalized Dimensions of Fractals and Strange Attractors." Physica D 8, 435, 1983.)

Quadrant (label axes)

Quadratic Field (Berg, E. Fysiogr. Sällsk. Lund. Föhr. 5, 1-6, 1935.; Oppenheim. Math. Ann. 109, 349-352, 1934.)

Quasigroup (numbers for each order)

Queen Graph (Gosset, T. [TITLE?] Mess. Math. 44, 48, 1914.; Jarnicki et al. 2015. Preprint)

Rabbit-Duck Illusion (Scheidemann, N. V. Experiments in General Psychology. Chicago, [PUBLISHER?] 1939 [AUTHOR?]. Fliegende Blätter. [VOLUME/NUMBER?], October 23, 1892, p. 147.)

Radial Curve (figure)

Ramanujan's Square Equation (Nagell, T. Nordisk Mat. Tidskr. 30, 62-64, 1948.)

Random Number (Janson Random number generators)

Rational Double Point (19 out of 20)

Rational Number (Bourbaki, N. Éléments de mathématique: Algèbre. [CITY, PUBLISHER, YEAR, PAGE?])

Rayleigh-Ritz Variational Technique (Rayleigh. "In Finding the Correction for the Open End of an Organ-Pipe." Phil. Trans. 161, 77, 1870)

Reciprocal Curve (Relation to the inverse curve?)

Reflection Triangle (ETC: a(-b^4+a^2b^2+c^2b^2-c^4+a^2c^2))

Regular Heptagon (Thébault, V. Mathesis, p. 204, 1913.; Thébault, V. Mathesis, p. 169, 1938.; Thébault, V. Mathesis, p. 344, 1950.; Thébault, V. Mathesis, p. 78 and 329, 1955.; Thébault, V. Mathesis, p. 106 and 149, 1956.)

Relatively Prime (Cesaro and Sylvester 1883; Sylvester 1909)

Remez Algorithm (Remez, E. Ya. "Sur le calcul effectif des polynômes d'approximation de Tschebyscheff." C. P. Paris, 337-340, [VOLUME?], 1934.)

Rep-Tile (Langford, C. D. "Uses of a Geometric Puzzle." Math. Gaz., No. 260, 1940)

Resultant (Sturmfels, B. [TITLE?] In Applications of Computational Algebraic Geometry (Ed. D. A. Cox and B. Sturmfels). Providence, RI: Amer. Math. Soc., [PAGES?] 1997.; Wee, C. E. and Goldman, R. N. [TITLE?] IEEE Comput. Graphics Appl. 69, [PAGES?] 1995.)

Reversal (Kraitchik, M. La Mathématique des Jeux. Brussels, pp. 55, 59, 1930.;)

Riemann Hypothesis (Stieltjes, T. [TITLE?] C. R. A. S. [VOLUME, PAGES?] 1885)

Riemann P-Differential Equation (Papperitz [INITIALS?]. [TITLE?] Math. Ann. 25, 213 [ENDING PAGE?], 1885.)

Riemann P-Series (Riemann, B. [TITLE?] Abh. d. Ges. d. Wiss. zu Göttingen 7, 1857. Reprinted in Mathematisch Werke, p. 67, 1892)

Riemann Prime Counting Function (Hardy, G. H. and Littlewood, J. E. [TITLE?] Acta Math. 41, 119-196, 1918.)

Riemann-Siegel Functions (Odlyzko, A. M. "The 10^(20)th Zero of the Riemann Zeta Function and 70 Million of Its Neighbors." Preprint.;)

Riemann Zeta Function (Check Stark 1974 formula (37); Odlyzko, A. M. "The 10^(20)th Zero of the Riemann Zeta Function and 70 Million of Its Neighbors." Preprint.; Bailey, D. H. "Multiprecision Translation and Execution of Fortran Programs." ACM Trans. Math. Software. [VOLUME, PAGES, YEAR?];)

Riemannian Geometry (Previato: Much of the treatment of Riemannian geometry relies on books address to engineers)

Root Linear Coefficient Theorem (reference)

Rotor (Uspekhi Mat. Nauk 3, No. 2 (24), 239, 1948)

Roundoff Error ([AUTHOR, TITLE?] The Toronto Star. [PAGES?] November 19, 1983.)

Routh-Hurwitz Theorem (The definition of Gradshteyn and Ryzhik uses b_k up to k=2n-1, but k only goes up to n)

Rule 62 (sloane: 1, 7, 25, 111, 433, 1751, 7033, 28047, 112305; sloane: 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1)

Rule 126 (sloane: 1, 7, 27, 127, 387, 1935, 6579, 32767; [not via superseeker] sloane: 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0,)

Rule 182 (sloane: 1, 7, 21, 127, 381, 1911, 5461; [not via superseeker] sloane: 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,)

Runge-Kutta Method (Kutta, M. W. [TITLE?] Z. für Math. u. Phys. 46, 435 [ENDING PAGE?], 1901. Lindelöf, E. [TITLE?] Acta Soc. Sc. Fenn. 2, [PAGES?] 1938. Runge, C. [TITLE?] Math. Ann. 46, 16 [ENDING PAGE?]7, 1895.)

Ruth-Aaron Pair (Drost, J. L. "Ruth/Aaron Pairs." J. Recr. Math. 28, No. 2, pp. 120-122, [YEAR?]; Peterson, I. "MathTrek: Playing with Ruth-Aaron Pairs." Sci. News 168, [PAGE RANGE?], Aug. 6, 2005.)

Saint Petersburg Paradox (Kamke, E. Einführung in die Wahrscheinlichkeitstheorie. Leipzig, Germany, pp. 82-89, 1932)

Sangaku Problem (Kimberling, C. "Review: Traditional Japanese Mathematics Problems from the 18th and 19th Centuries and Japanese Temple Geometry Problems.)

Schlömilch Remainder (Roche. Mem. de l'Acad. de Montpellier. 1858.)

Schlömilch's Series (Chapman. Quart. J. 43, 34-37, 1912.; Schlömilch. Z. für Math. Phys. 3, 137-165, 1857.)

Schoute's Theorem (Not found as cited (two times): Schoute, P. H. Proc. Amsterdam Acad., 39-62, 1887-1888)

Schur Number (add Guy references)

Seiffert's Spherical Spiral (Seiffert. "Über eine neue geometrische Einführung in die Theorie der elliptischen Funktionen." Wissensch. Beiträge Jahresber. Städtischen Realschule zu Charlottenburg, Ostern. 1896.)

Self-Avoiding Walk ([AUTHOR?] Problem E185. Amer. Math. Monthly 44, 50-51, 1937.;)

Self Number (Kaprekar, D. R. The Mathematics of New Self-Numbers. Devaiali, pp. 19-20, 1963.)

Semiperimeter (add dotted lines)

Separation Theorem (the function should be specified as well as what the lambda_v represent.)

Sierpiński's Composite Number Theorem (Keller, W. "Factors of Fermat Numbers and Large Primes of the Form k·2^n+1, II." Preprint available at http://www.rrz.uni-hamburg.de/RRZ/W.Keller/)

Similar (Neuberg and Tarry. Mathesis 2.)

Similitude Center ([AUTHOR?] Problem 2819. Amer. Math. Monthly 28, 229-230, 1921.)

Simple Function (add diagram graph of a simple function)

Sine (Beylkin, G. and Mohlenkamp, M. J. [TITLE?] Proc. Nat. Acad. Sci. USA 99, 10246 [PAGE RANGE?], 2002.;)

Sine-Triple-Angle Circle (Tucker and Neuberg, J. Mathesis 12, 1887. [Cited as "M, 1887-12"])

Siteswap (looks underlined after latex2html gets through with it!)

Skewes Number (Asimov, I. "Science: Skewered!" Mag. Fantasy Sci. Fiction [VOLUME, PAGES?] Nov. 1974.)

Smith's Markov Process Theorem (find a reference and check)

Soddy Circles (Fillmore, J. P. and Paluszny, M. Seminarberichte Mathematik Fernuniversität Hagen 62, 45, 1997.; Martini, H. In Geometrie und ihre Anwendungen (Ed. O. Giering and J. Hoschek). Munich, Germany: Carl Hanser, 1994.; Söderberg, B. Phys. Rev. A 46, 1859, 1992.; Study, E. Math. Ann. 49, 497, 1897.;)

Soldner's Constant (Soldner. Abhandlungen 2, 333, 1812.)

Solid of Revolution (ADD: Barrels by cylinders)

Spencer's Formula (Spencer, J. J. I. A. 38, 334, 1904. Spencer, J. J. I. A. 38, 339, 1904. Spencer, J. J. I. A. 41, 361, 1907.)

Sperner's Lemma (add figure)

Spherical Covering (Hardin, R. H.; Sloane, N. J. A. S.; and Smith, W. D. Spherical Codes. In preparation.)

Square Point Picking (Bailey, D. H.; Borwein, J. M.; and Crandall, R. E. "Box Integrals." Preprint. Apr. 3, 2006.)

Square Triangle Picking (Seidov, Z. F. [TITLE?] [DATE?] 2000. http://axchiv.org/abs/math.GM/0002134/)

Standard Map (Hermann; Italians; Greene; Mather)

Star of David Theorem (Gould, H. W. [TITLE?] Not. Amer. Math. Soc. 19, A-685, 1972 Hitotumatu, S. and Sato, D. "Expansion of the Star of David Theorem." Abstracts Amer. Math. Soc., p. A-377 [ENDING PAGE?], 1975. Sato, D. "Expansion of the Star of David Theorem of H. W. Gould and David Singmaster." Abstracts Amer. Math. Soc., p. A-377 [ENDING PAGE?], 1975.)

State Diagram (Abbott, R. "The Farmer Goes to Market." Sci. Amer. [Volume?], [Page range?], Oct. 1962.)

Steiner-Lehmus Theorem (Neuberg, J. Bibliographie du triangle et du tétraèdre. p. 337, 1923.)

Steiner Points (Neuberg, J. "Sur le point de Steiner." J. de math. spéciales, p. 29, 1886.)

Stella Octangula (Kepler, J. "Harmonice Mundi." In Opera Omnia, Vol. 5. Frankfurt, 1864.)

Stieltjes Integral (Pollard, S. Quart. J. Math. 49, 73-138, 1923.;)

Stirling's Approximation (Stirling, J. Methodus differentialis. 1730.)

Strophoid (add figure)

Student's t-Distribution (Shaw, W. "New Methods for Managing 'Student's' T-Distribution." Submitted to J. Comput. Finance.)

Sturm Function (Sturm, C. "Mémoire sur la résolution des équations numériques." Bull. des sciences de Férussac vol. 11, 1929. quoted in Dörrie p. 112)

Subfactorial (Whitworth, W. A. Messenger Math. 1878;)

Subresultant (Hong, H. "Subresultants in Roots." Submitted 1999.)

Symmetric Graph (more terms: 0, 0, 1, 2, 2, 5, 2)

Tait's Hamiltonian Graph Conjecture (Sachs, H. "Ein von Kozyrev und Grinberg angegebener nicht-Hamiltonischer kubischer planarer Graph." In Beiträge zur Graphentheorie. [EDITOR, CITY, PUBLISHER?] pp. 127-130, 1968.)

Tau Function (Darling, H. B. C. Proc. London Math. Soc. 19, 350-372, 1921. Jennings, D. Ph.D. thesis. Southampton, 1993. Jordan, B. and Kelly, B. III. "The Vanishing of the Ramanujan Tau Function." Preprint, 12 Mar 1999. Lehmer 1949 Ramanujan, S. Proc. London Math. Soc. 18, 1920. Swinnerton-Dyer 1973)

Taylor Circle (Taylor, H. M. Proc. London Math. Soc. 15.)

Taylor's Theorem (Cox, H. [TITLE?] Cambridge and Dublin Math. J. 6, 80 [ENDING PAGE?], 1851.; Taylor 1715 reference; Gregory 1670-1680 reference)

Tetrahedron (Wells, D. "Puzzle Page." Games and Puzzles. Sep. 1975.)

Tetrix (change rotation and scaling of third figure to be same as first two)

Thâbit ibn Kurrah Rule (Gérardin Sphinx-Oedipe 1907-8, 49-56, 65-71; Gérardin Assoc. Franç avanc. sc. 37, 1908, 36-38; Gérardin l'intermédiaire des math. 1909, 104 Woepcke, F. J. Asiatique 20, 320-429, 1852.;)

Thomson Cubic (Thomson, F. D. [TITLE?] Educ. Times. [PAGES?] [ISSUE/VOLUME?] Aug. 1864.)

Tiling (Gardner, M. Penrose Tiles to Trapdoor Ciphers. Washington, DC: Math. Assoc. Amer.; Abas)

Torsional Rigidity (Dinnik, A. [TITLE?] Bull. Don. Polytech. Inst. Vovotcherkassk 1, 309 [ENDING PAGE], [YEAR?]; Galerkin, B. G. "Torsion of a Triangular Prism." Izv. Akad. Nauk, SSSR [VOLUME?] pp. 111-118, 1919.; Greenhill, A. G. [TITLE?] Messenger Math. 9, 35 [ENDING PAGE?], 1879.; Saint-Venant. [ITIIALS?] [TITLE?] Compt. Red. 87, 849 and 903 [FULL PAGE RANGES?], 1878.)

Totient Function (Kendall, D. G. and Osborn, R. "Two Simple Lower Bounds for Euler's Function." Texas J. Sci. 17, [PAGES?], 1965.)

Transcendental Number (Allouche, J. P. and Shallit, J. In preparation.)

Triangle Geometry (Kimberling, C. "Transfigured Triangle Geometry." Preprint. Mar. 5, 2005.)

Triangle Line Picking ( Pure, R.; Durran, S.; Tong, F.; Pan, J. "Distance Distribution Between Two Random Points in Arbitrary Polygons." To appear in Math. Meth. Appl. Sci.)

Triangular Number (Cesaro 1886)

Trigonometric Addition Formulas (Nelson, R. To appear in College Math. J., March 2000.)

Trilinear Coordinates (Wong, M. K. F. Int. J. Math. Educ. Sci. Tech. 27, 293-296, 1996. Wong, M. K. F. Int. J. Math. Educ. Sci. Tech. 29, 143-145, 1998.)

Triply Periodic Function (Jacobi, C. G. J. [TITLE?] J. für Math. 13, 55-56, 1835.)

Triskaidekaphobia (Coriat, I. H. Abnormal Psychology 2, [PUBLISHER, PAGE RANGE?] vi, p. 287, 1911.; Scanlon, T. J. et al. "Is Friday the 13th Bad for Your Health?" Brit. Medical J. [VOLUME?], 1584-1586, Dec. 18-25, 1993.)

Truchet Tiling (are the exact circle and dumbbell fractions known?)

Tschirnhausen Transformation (Tschirnhaus. Acta Eruditorum. 1683.)

Tutte's Graph (Sachs, H. "Ein von Kozyrev und Grinberg angegebener nicht-Hamiltonischer kubischer planarer Graph." In Beiträge zur Graphentheorie. [EDITOR, CITY, PUBLISHER?] pp. 127-130, 1968.)

Twin Prime Cluster (Mudge, M. "Some Sequences of Smarandache Contrasted with a Permutations Problem Relating to Class/student Allocation." Personal Computer World, London, England. [VOLUME?] pp. 674-675, June 1995.; Mudge, M. "Smarandache Sequences and Related Open Problems." Personal Computer World. [VOLUME, PAGES?] Numbers Count, February 1997.)

Twin Primes (Ricci; Pil'Tai 1972; Atkin and Richert. Amer. Math. Soc. Not. 26, A-373, 1979. Ruiz. To be published in Math. Gaz. 2000 Glaisher 1878)

Twinplex Graph (Robertson, N.; Seymour, P.; and Thomas, R. "Excluded Minors in Cubic Graphs." J. Combin. Th., Ser. B. In press, Feb. 2019.)

Uniform Convexity (add figure a la Cheney 1966, p. 21, with two end points on an ellipse (which is uniformly convex) and on an octagon, (which isn't))

Vertex Triangle (Kimberling, C. "Transfigured Triangle Geometry." Preprint. Mar. 5, 2005.)

Vieta's Formulas (Viète, F. Opera mathematica. [CITY, PUBLISHER?] 1579.)

von Mises Distribution (any idea how to calculate the mean or circular variance?)

Voting Paradoxes (Lipton, R. G.; and Widgerson, A. "Multi-Party Cryptographic Protocols."; Riker, W. H. "Voting and the Summation of Preferences." Amer. Political Sci. Rev., Dec. 1961. Saari, D. G. Math. Intell. 10, 32, 1988.)

Wavelet (REWRITE)

Weighing (Strong, C. L. "The Amateur Scientist: How to Make an Aerodynamic Smoke Tunnel and More about the Puzzle of the 12 Balls." Sci. Amer. 192, [PAGE RANGE?], May 1955.; MacMahon, P. A. Quart J. Math. 21, 367-373, 1886.; Descartes, B. Eureka, No. 13, Oct. 1950; Tweedle, M. C. K. Math. Gaz. 23, 278-282, 1938.; Nature 42, 113-114, Dec. 4 1890)

Weill Point (Weill. Liouville's J. (Ser. 3) 4, 270, 1878.)

Weill's Theorem (Casey, J. Quart. J. Pure Appl. Math. 5, 44, 1862.; Weill. Liouville's J. (Ser. 3) 4, 270, 1878.)

Weyrich's Formula (check this; it doesn't seem right)

Wiener Numbers (Wiener, N. "The Spectrum of an Array and Its Applications to the Study of the Translation Properties of a Simple Class of Arithmetical Functions." J. Math. Phys. 6, [PAGES?] 1926-1927.)

Wilkie's Theorem (check formula)

Wilson Polynomial (Check Koepf's definition)

Wilson Prime (Gonter, R. H. and Kundert, E. G. "All Numbers Up to 18876041 Have Been Tested without Finding a New Wilson Prime." Preprint, 1994.)

Wulff Shape (Wulff, G. "Zur Frage der Geschwindigkeit des Wachstums und der Auflösung der Krysallflagen." Z. Kryst. Mineral. 34, 449, 1901.)

Z (Bourbaki, N. Éléments de mathématique: Algèbre. [CITY, PUBLISHER, YEAR, PAGE?])

Zonohedron (Fedorov, E. S. Zeitschr. Krystallographie und Mineralogie 21, 689, 1893.)

Zsigmondy Theorem (Chabaud, F. and Vaudenay, S. "Links between Differential and Linear Cryptanalysis." EUOROCRYPT 94, pp. 356-365, [PUBLISHER, CITY?] 1994.)