Although the principle of these kinds of “vanish puzzles” is really quite simple, they still confound countless numbers of puzzle enthusiasts!
Imagine the wheels of your bike are polygons. Then, to ride smoothly the road should be made of ‘catenaries‘ (yes, those bumpy things).
Intriguing linear motion perceived as circular motion! Watch as the black balls rotate in a circle, then focus on one ball at a time and you will notice that it follows a straight line. Also, watch at the moment when there are only four balls moving, it forms a rotating square between the four balls. This is just neat example of looking deeper into something so simple and discovering a hidden pattern.
Pattern with Arabesque paths moving in a linear fashion induces rotational motion to a hexagonal device.
There are many fun facts regarding the factorials. For instance:
It is possible to “peel” each layer off of a factorial and create a different factorial, as shown in the neat number pattern below. A prime pattern can be found when adding and subtracting factorials. Alternating adding and subtracting factorials, as shown in the picture, yields primes numbers until you get to 9! Continue reading ““Magic” Factorials”
Given 3 circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy: ace/bdf = 1
In any triangle, the 3 points of intersection of the adjacent angle trisectors ALWAYS form an equilateral triangle (in blue), called the Morley triangle.
Amazingly, this sequence of fractions converges to 0.70710678118…, or to be precise, to √2/2. The sequence is related to the Prouhet-Thue-Morse sequence.
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.
This problem is related to the Egyptian fractions.
Showing why a doughnut and a mug are topologically equivalent…