Here is another geometrical Op Art of my creation: “Deep Blue” (2001). The yellowish scintillating rays you see in this picture are a construct of your brain. This work is available as prints from Saatchi Art gallery. ## Brahmagupta’s Theorem

If a cyclic quadrilateral ( = with vertices lying on a common circle) has diagonals which are perpendicular, then the perpendicular to a side from the point of intersection of the diagonals will bisect the opposite side (AF = FD). ## Amazing Roman Rock-crystal Icosahedron Die

Here is an intriguing Roman crystal 20-sided die (icosahedron), used in fortune-telling, ca. 1st century AD.

## Possible Impossible Cube

Is it possible to 3D print an impossible cube ? Here is a way to do it… After all, it’s all about perspective! Source: Wolfram Community

## A Neat Geometrical Illusion: The Scintillating Starburst

As you maybe know, I am an expert in optical illusions… So, I would like to show you one of my oldest illusions I created in the 90s. In the picture you may see ghost-like dark radial beams. This illusion is a variant of the Herman’s scintillating grid illusion. I designed this illusion just by turning 45 degrees the Herman grid and then by applying a polar transformation.

## Exterior Angles

In a polygon, an exterior angle is formed by a side and an extension of an adjacent side. The sum of exterior angles in any convex polygon always adds up to 360 degrees, as shown in the 2 visual proofs below. Therefore, for all equiangular polygons, the measure of one exterior angle is equal to 360 divided by the number of sides in the polygon.  ## Kepler Triangle

A Kepler triangle is a right triangle formed by three squares with areas in geometric progression according to the golden ratio.
So, the sides of such a triangle are in the ratio 1 : √ φ : φ [where φ = ( 1 + √5 )/ 2 is the golden ratio.] ## A Magic Right Triangle

A triangle with sides π (3.14), e (2.71), and the Golden Ratio (1.61) is almost a right triangle! ## Archimedes’ turbine

Geometric composition involving equilateral triangles 