Linear to rotational motion

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.

Linear to circular motion

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Pattern with Arabesque paths moving in a linear fashion induces rotational motion to a hexagonal device.

“Magic” Factorials

There are many fun facts regarding the factorials. For instance:

  • 0! = 1 by convention. As weird as it may sound, this is a fact that we must remember.
  • The number of zeroes at the end of n! is roughly n/4.
  • 70! is the smallest factorial larger than a googol.
  • The sum of the reciprocals of all factorials is e.
  • Factorials can be extended to fractions, negative numbers and complex numbers by the Gamma function.

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”

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