## Archimedes’ turbine

Geometric composition involving equilateral triangles ## IXOHOXI Magic Square

The neat magic square featured on this stamp was created by Brazilian mathematician Inder Taneja. This square, called IXOHOXI magic square, not only shows common properties like other magic squares, as well as being pandiagonal, but also include extra properties such as symmetries, rotations and reflections. ## Shortest Path on a Cube

The regular hexagon hidden in a cube unfolds to a straight line on a net of the cube.

पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते ॥
“Removing infinity from infinity, leaves infinity” ## Magic Inscribed Lotus

Indian mathematician Nārāyaṇa (1356) is the originator of the “Inscribed Lotus” (Padma Vrtta, a magic diagram constructed with the numbers of the 12×4 magic rectangle), in which every group of 12 numbers has the same sum 294. Continue reading “Magic Inscribed Lotus”

A strange right-triangle involving the unit imaginary number i ## Sacred Geometry

Repeated barycentric subdivision results in a gorgeous fractal-ish pattern. ## Toeplitz’ Conjecture

Does every simple closed curve in the plane contain the vertices of a square?
No one knows, but the answer to this question is positive if the curve is sufficiently regular.
Take 6 points on a circle such that every second edge (green chords) has length equal to the radius of the circle. Then the midpoints of the other three sides of the cyclic hexagon form an equilateral triangle. A 3D regular hexahedron solid (cube) passing through a 2D plane: 