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
A Curious Constant
A palindromic number is an integer that remains the same when its digits are reversed. The sum of the reciprocals of all the palindromic numbers in the world converges to approximately 3.3703…
Analog Binary-to-Decimal Converter
This is a simple linkage-mechanism for converting binary numbers to decimal numbers.
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.
Harshad number is defined as an integer that is divisible by the sum of its digits.
Interestingly, the years 2022-2025 are Harshad numbers. It is worth noting that having more than two consecutive Harshad years is a rare occurrence. The last time it occurred was over 1000 years ago for years 1014-1017. The next time it is expected to occur after 1000+ years will be during the years 3030-3033.
A Lucky Year!
7⁷ mod 7! = 2023 what a lucky year…
More amazing number patterns for getting 2023: https://community.wolfram.com/groups/-/m/t/2749012
The Puzzling Ramanujan’s Magic Square
As you maybe know, a magic square is a square divided into smaller squares each containing a number, such that the figures in each vertical, horizontal, and diagonal row add up to the same value.
In this particular magic square by Ramanujan, fields of the same color add up to 139. The first row – highlighted in the bottom-right magic square – shows his date of birth.
Some remarkable summation formulas…
Because Fn→ φⁿ when n→ ∞