Haruki’s Theorem

Given 3 circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy: ace/bdf = 1

Haruki's theorem

Prime Fractions

Did you know? You can write the number 1 as a sum of 48 different fractions, where every numerator is 1 and every denominator is a product of exactly two primes.

Prime fractions equal one

Very Large Numbers In Real Life

Százmillió-B. pengő
Százmillió-B. Magyar Pengő

Most people know about Zimbabwe’s trillion dollar bill notes or have heard stories about Germans using worthless Marks during the Weimar Republic for wallpaper, but what few realize is that Hungary broke all the records. Just after the WWII, between 1945 and 1946, Hungary was in a state of hyperinflation, with inflation rates reaching 41.9 quintillion percent (that is 41,900,000,000,000,000,000%). Continue reading “Very Large Numbers In Real Life”

Math-Magic Vanishing Space

Inspired from the astrological tables, here is a new puzzle of my creation designed according to the ‘Golden Number Rules’, which is reflected in the proportion of each single piece of the game. Thanks to the balanced dimensions of its pieces, this puzzle acquires some intriguing magical properties!

This “math-magical” puzzle is composed of a tray in which the pieces are assembled.

Quadrix puzzle 2 Continue reading “Math-Magic Vanishing Space”

Bidimensional Müller-Lyer Illusion

I am working on a new two-dimensional variant of the Müller-Lyer illusion… You may be surprised to know that the Müller-Lyer illusion isn’t only linear: it involves plane geometry too! In fig. A shown below, the ends of the blue and red collinear segments, arranged in a radial fashion around a central point, delimit two perfectly concentric circles. However, for most observers, they seem instead to define a large ovoid that circumscribes another one, slightly eccentric (Fig. B). This comes from the fact that the red segments seem to stretch towards the lower part of the figure, while the blue segments seem to stretch towards the upper part of the same. As you can see, in this variant comes also into play the “neon color spreading” effect. In fact, a bluish inner oval-like shape appears within the black arrow heads (Fig. A), though the background is uniformly white.

Müller-lyer ovoid

Continue reading “Bidimensional Müller-Lyer Illusion”

How to ‘magically’ untie a shoelace double knot

Topology is a fascinating branch of mathematics that describes the properties of an object that remain unchanged under continuous “smooth” deformations. Actually, many 3D puzzles are based on topological principles and understanding some very basic principles may help you analyze whether a puzzle is possible or not.

Puzzle-Meister G. Sarcone created this amusing everyday-life topological puzzle to help children to easily take their shoes off.

image knots

As you know, the standard shoelace knot is designed for quick release and easily comes untied when either of the working ends is pulled. Thus, most people think that tying a shoelace into a double knot is an effective method of making the knot “permanent”. But is it true? Continue reading “How to ‘magically’ untie a shoelace double knot”