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Is a Soccer ball just a ball?

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Even though this question might seem simple, a soccer ball isn’t a “ball”, as many people think. 

As crazy as it may sound, “A soccer is a Polyhedron”.

Polyhedron

A polyhedron is a three-dimensional shape with flat faces, straight edges, and sharp corners (vertices). The term “polyhedron” derives from the Greek words poly, meaning “many,” and hedron, meaning “surface.” When many flat surfaces are joined together, a polyhedron is formed. The names of these shapes are based on their faces, which are typically polygons.

It’s a truncated, 32-sided icosahedron with both pentagonal and hexagonal surfaces. It has 60 vertices and is one of the least known and most widely used shapes in the entire world. This is the geometry of soccer.

It has 20 hexagons and 12 pentagons on it.

A short video summarises this:

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Math titbits

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For example:

If we consider the three consecutive numbers 7,8 and 9

82 = 64

7 X 9 = 63.

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Five Postulates of Euclidean Geometry

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The elements of geometry, an exquisite and influential geometry treatise written around 300 B.C by the Greek mathematician Euclid, explains Euclidean geometry.

The five postulates form the foundation of euclidean geometry.

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Attoseconds

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Atto means eighteenth in Danish, Attosecond means 1/1,000,000,000,000,000,000th of a second.

In one attosecond, light can travel the length of 3 hydrogen atoms.

Generally, light can travel 7.5 times around the earth in 1 second. However, in an attosecond it can barely move from one end of the molecule to the other end.

Another way to think about this is:

one attosecond : one second = one second : 32 billion years.

The Flash, a superhero from a comic book who has the ability to run faster than the speed of light, has the ability to see events that occur for less than one attosecond, which, for humans, is less time than it takes to blink an eye.

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Seconds in 6 weeks=10!

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We know that, for any positive integer n, n! is defined as the product of all positive integers less than or equal to n.

i.e., n! = 1 x 2 x 3 x … x (n-1) x n

so, 10! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 = 3,628,800

we see that, how seconds in 6 weeks make 10!

6 weeks = 6 x 7 days = 6 x 7 x 24 hours = 6 x 7 x 24 x 60 minutes = 6 x 7 x 24 x 60 x 60 seconds = 3,628,800 seconds

This video verifies that seconds in 6 weeks = 10!

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Cut a cake into eight equal pieces by using only three cuts.

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1.Two cuts should make a cross on the surface of the cake, therefore splitting it into four equal halves

2. Third cut as a horizontal slit through the cake’s center.

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Is √2 irrational?

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Yes it is.

Hippasus, a Greek philosopher who was an early disciple of Pythagoras, is credited with being the first person to discover the existence of irrational numbers.

However, many of Pythagoras’s disciples couldn’t wrap their heads around the concept of irrational numbers and also couldn’t contradict Hippasus with reasoning.

He was drowned to death upon Pythagoras’ command.

The proof is by contradiction.

First let us assume that √2 is rational.

This means that, x/y = √2, where x and y have no common factors.

Squaring on both sides, we get:

x2 /y2 = 2

x2 = 2y2 (The number is even on the right-hand side. Because any number multiplied by 2 is always even.)

The only way the equation to be true is that x itself should be even.

Thus x2 is even and it is divisible by 4.

Therefore, x and y are even numbers with common factors. This contradicts our assumption that x and y have no common factors.

Therefore, √2 cannot be rational.

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Pythagoras constant

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The square root of 2 is written as √2. The square root of 2 is often known as root 2, radical 2, or the Pythagoras constant.

Additionally, it is the first irrational number to ever be identified.

Geometrically,

Consider a square with side length 1, and the need to determine the diagonal length.

The formula for the diagonal of a square is derived using the Pythagoras theorem.

The length of a diagonal across a square with sides of one unit of length is equal to the √2.

The value of √2 up to 15 decimal places is 1.414213562373095…The value of √2 is currently known to 1 trillion decimal places.

An intriguing fact about paper sizes is that they are dependent on √2.

The international paper size standard ISO 216 (International Organisation for Standardisation) is the standard that paper sizes are all based on.

In the ISO paper size system, the height-to-width ratio of all pages is the square root of two (1.4142 : 1). In other words, the width and the height of a page relate to each other like the side and the diagonal of a square.

  • Non-terminating, non-repeating decimal representation.
  • The first irrational number identified was the number √2.
  • √2 is also called as the Pythagoras constant.
  • √2 represents the diagonal of a unit square.
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Honey bees and Hexagons

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When bees construct honeycombs, they do it in a hexagonal layout.

bee and beehive

The honeycomb’s hexagonal structure, which can be used to store honey, pollen, or eggs, is created out of wax by the bees.

Hexagons are a common shape used by bees. So why not go with a more simple shape like a circle, triangle, or square?

A tiling is any pattern that repeats but doesn’t overlap on a flat surface. A tessellation is another word for tiling.

The three geometrical figures with equal sides can fit together on a flat surface without leaving gaps: equilateral triangles, squares, and hexagons.

Of these three Hexagon has the least perimeter. That’s why nature has chosen the hexagon shape.

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Kaprekar Number

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A Kaprekar number is

A number’s square divided into two parts such that the sum of its parts is equal to the original number.

Kaprekar Number

An example of this Kaprekar Number is explained in the following video.

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Geometry Golden Ratio Math around us math facts Mathematical patterns Number theory

Metallic Ratios: The Hidden Family of Magic Numbers

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The Mathematics Behind Sudoku

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Geometry Math around us math facts Math titbits

Happy Pi Day 2026!