## Ghost Colors

This is one of my earliest color optical illusions. There is no yellow or green in the diamond shapes, just vertical black lines! (If you don’t believe it, use a eyedropper tool to check it.)

## Right Triangle with Rational Sides

The simplest right triangle with rational sides (the longest side has a denominator of 45 digits!) and area 157, was found by Don Zagier in 1993. 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.] 