### 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

By the Pythagorean theorem, adjacent cubes with side length 1 produce square roots of the first six natural numbers, as shown below…

Amazingly, if we add 3 extra cubes, we can extend the series of square roots of natural numbers up to √14 (excluding √7)

Harshad number is an integer divisible by the sum of its digits.

Curiously enough, the years 2022-2025 are Harshad numbers. More than 2 consecutive Harshad years is so rare that it last happened 1000+ back for years 1014-1017. And will next happen after 1000+ years in 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.

### Summation Formulas

Some remarkable summation formulas

### φibonacci formula

Because Fn→ φ when n→ ∞

### When matrices meet Fibonacci

F0 = 1, F1 = 1, Fn = 1, Fn = Fn-1+ Fn-2, n ≥ 2

### 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…