In 1937, mathematician Victor Thébault found that squares constructed on a parallelogram’s sides yield a square when their centers are connected.
Read more: https://en.wikipedia.org/wiki/Th%C3%A9bault’s_theorem
Thébault’s Theorem
Fibonacci Zoetropes
The Fibonacci Zoetropes are sculptures by John Edmark. The spirals in the sculptures follow the Fibonacci sequence. When filmed at 24 frames per second and spun at 550 revolutions per minute, each frame represents a 137.5 degree rotation, which is equivalent to the Golden Angle.
Arithmetic Mean ≥ Geometric Mean
A simple yet neat visual proof demonstrating that the arithmetic mean of two positive numbers ‘a’ and ‘b’ is always greater than or equal to their geometric mean, symbolically represented as (a+b)/2 ≥ √ab
Amazing Double Cube
According to the Pythagorean theorem, adjacent cubes with side length 1 produce square roots of the first six natural numbers, as illustrated below:
Remarkably, by adding three extra cubes, we can extend the series of square roots of natural numbers up to √14. However, to obtain the square root of 7 using this method, we need to extend our analysis to a 4-dimensional world.
When Mondrian meets Pythagoras & Fibonacci
The side of medium white square / side of small black square = golden ratio, which is the limit of the ratio of consecutive Fibonacci numbers…
This geometric op art is available as prints and posters from our online gallery.
Knot, knot, who’s there? Topology…
Lebrecht Goeritz was a German mathematician who designed some trivial knots almost a century ago. His most famous unknot has eleven crossings.
Visual Calculus
Mamikon A. Mnatsakanian (Armenian: Մամիկոն Մնացականյան) devised in 1959 a visual method to show that the areas of two annuli with the same chord length are the same regardless of inner and outer radii.
As an undergraduate, Mamikon specialized in the development of geometric methods for solving calculus problems by a visual approach that makes no use of formulas, which he later developed into his system of visual calculus.
Geometry & Electronics
Geometric shapes are not limited only to the figurative aspect, they can also play active roles, for instance, serving in microelectronics to build operational printed circuits such as: small inductors (magnified, fig. a below), resistors (fig. b) and capacitors (fig. c). (image taken from my book “Almanach du Mathématicien en Herbe“)
Paradoxical Elastic Squares
A math-magic article I wrote for the German magazine Zeit Wissen: with the 13 triangular and square pieces (fig. 1) it is possible to form two large squares shown in fig. 2. Though the second large square has an extra piece the dimensions of the squares seem to be the same! Can you explain why this is possible?
This puzzle is available as greeting cards from my online store.
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.)
