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A construction done using only a straightedge. The Poncelet-Steiner theorem proves that all constructions possible using a compass and straightedge are possible using a ...

The Steiner inellipse, also called the midpoint ellipse (Chakerian 1979), is an inellipse with inconic parameters x:y:z=a:b:c (1) giving equation ...

Two points z and z^S in C^* are symmetric with respect to a circle or straight line L if all circles and straight lines passing through z and z^S are orthogonal to L. Möbius ...

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...

Consider two directly similar triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 with B_1C_1:A_1C_1:A_1B_1=B_2C_2:A_2C_2:A_2B_2=a:b:c. Then a·A_1A_2, b·B_1B_2 and c·C_1C_2 form the ...

A compact set W_infty with area mu(W_infty)=8/9(24)/(25)(48)/(49)...=pi/4 created by punching a square hole of length 1/3 in the center of a square. In each of the eight ...

The equation of motion for a membrane shaped as a right isosceles triangle of length c on a side and with the sides oriented along the positive x and y axes is given by where ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

There are three types of cubic lattices corresponding to three types of cubic close packing, as summarized in the following table. Now that the Kepler conjecture has been ...

If p is a prime number and a is a natural number, then a^p=a (mod p). (1) Furthermore, if pa (p does not divide a), then there exists some smallest exponent d such that ...