Useless, yet intriguing arithmetical fact… Multiplying this large number by 2, the rightmost digit 2 seems to pop to the front.
Such numbers are called “parasitic numbers“, read more: https://en.wikipedia.org/wiki/Parasitic_number
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.
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.
Continue reading “Amazing Roman Rock-crystal Icosahedron Die”
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
Perfect “Square” Circle
Numbers 1 to 32 are placed along the circumference of a circle without repeating any number and still the sum of any two adjacent numbers in this circle is a perfect square!
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.
Continue reading “A Neat Geometrical Illusion: The Scintillating Starburst”
Sum of Consecutive Cubes (Visual Proof)
The sum of the first n cubes is the square of the nth triangular number:
13 + 23 + 33 + 43 + 53 + . . . + n3 = (1 + 2 + 3 + 4 + 5 + . . . + n)2.
