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

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# Archimedes Lab Project

## Posts

### Parasitic Number

### Ghost Colors

### Right Triangle with Rational Sides

### Illusive Color Radial Beams

### Brahmagupta’s Theorem

### Amazing Roman Rock-crystal Icosahedron Die

### Possible Impossible Cube

### Perfect “Square” Circle

### A Neat Geometrical Illusion: The Scintillating Starburst

### Sum of Consecutive Cubes (Visual Proof)

Inspiring and Creative Resources & Tutorials for Science-Curious People

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

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.)

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**.

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).

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”

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

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!

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”

The sum of the first *n* cubes is the square of the *n*th triangular number:

1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3} + . . . + *n*^{3} = (1 + 2 + 3 + 4 + 5 + . . . + *n*)^{2}.