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.)
Ghost Colors
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.
Illusive Color Radial Beams
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.
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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.
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Edible Geometry.
The tutorial of the day: Turn a carrot into a cube-octahedron!
More edible geometry from: https://www.archimedes-lab.org/pastashape.html
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.]