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The intersection of an ellipse centered at the origin and semiaxes of lengths a and b oriented along the Cartesian axes with a line passing through the origin and point ...

A fractal based on iterating the map F(x)=ax+(2(1-a)x^2)/(1+x^2) (1) according to x_(n+1) = by_n+F(x_n) (2) x_(y+1) = -x_n+F(x_(n+1)). (3) The plots above show 10^4 ...

A constant appearing in formulas for the efficiency of the Euclidean algorithm, B = (12ln2)/(pi^2)[-1/2+6/(pi^2)zeta^'(2)]+C-1/2 (1) = 0.06535142... (2) (OEIS A143304), where ...

P_y(nu)=lim_(T->infty)2/T|int_(-T/2)^(T/2)[y(t)-y^_]e^(-2piinut)dt|^2, (1) so int_0^inftyP_y(nu)dnu = lim_(T->infty)1/Tint_(-T/2)^(T/2)[y(t)-y^_]^2dt (2) = <(y-y^_)^2> (3) = ...

A surface given by the parametric equations x = A(u-a)^m(v-a)^n (1) y = B(u-b)^m(v-b)^n (2) z = C(u-c)^m(v-c)^n. (3)

The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by (x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1, (1) where ...

The prime zeta function P(s)=sum_(p)1/(p^s), (1) where the sum is taken over primes is a generalization of the Riemann zeta function zeta(s)=sum_(k=1)^infty1/(k^s), (2) where ...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...

The circle passing through the isodynamic points S and S^' and the triangle centroid G of a triangle DeltaA_1A_2A_3 (Kimberling 1998, pp. 227-228). The Parry circle has ...

A right strophoid is the strophoid of a line L with pole O not on L and fixed point O^' being the point where the perpendicular from O to L cuts L is called a right ...