2022

Attoseconds

umasundresh 15 Dec 2022 No Comments

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.

Mathematicians

Fictional Mathematicians

umasundresh 8 Nov 2022 No Comments

Get to know some mathematicians whose whole existence was conjured up by the authors’ vivid imaginations.

Fictional Mathematicians

3 dimensional geometry 3Dimensional Geometry Geometry

Platonic Solids

umasundresh 3 Nov 2022 No Comments

Platonic solids are three-dimensional geometrical objects that have been studied for millennia due to their symmetry and beauty. Euclid, a Greek Mathematician proved that there are exactly five such solids.

They are a tetrahedron, a cube, an octahedron, a dodecahedron, and an icosahedron.

Regular polygons are those with all of their sides equal. Since a Regular Polygon has equal sides, it also has equal angles.

Number of sides ‘n’	Regular Polygon
3	Equilateral Triangle
4	Square
5	Pentagon
6	Hexagon

and so on…

A Platonic solid is a three-dimensional shape, each face is a regular polygon, and the same number of polygons intersect at each vertex.

There are only five Platonic solids exist.

1. Cube

The cube consists of 6 squares
Three squares meet at each vertex
8 vertices
12 edges

2. Tetrahedron

The Tetrahedron consists of 4 Equilateral triangles.
Three triangles meet at each vertex.
4 Vertices
6 Edges

3. Octahedron

The Octahedron consists of 8 triangles
4 triangles meet at each vertex
8 Faces
6 Vertices
12 Edges

4. Dodecahedron

The dodecahedron consists of 12 Pentagons.
3 pentagons meet at each vertex
20 Vertices
30 Edges

5. Icosahedron

The Icosahedron consists of 20 Equilateral triangles.
5 triangles meet at each vertex
12 Vertices
30 Edges

math facts Riddles

Seconds in 6 weeks=10!

umasundresh 18 Oct 2022 No Comments

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!

math facts Math Puzzle Math titbits

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

umasundresh 17 Oct 2022 No Comments

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.

ALGEBRA Applications

Applications of Logarithm in real life

umasundresh 14 Oct 2022 No Comments

In science, logarithm is used for many different things.

Some of the most common uses are to measure loudness (in decibels), earthquake intensity (on the Richter scale), radioactive decay, and acidity (pH = -log10[H+]).

Logarithms are also used to solve problems that involve exponential growth.

The following video summarizes the applications of logarithm in real life.

Applications of logarithm in real life

ALGEBRA

Cyclic Numbers

umasundresh 24 Sep 2022 No Comments

A cyclic number is a number of “n” digits that when multiplied by 1, 2, 3, …, n results in the same digits but in a different order.

Let’s find out whether 142857 is a cycling number or not

Here the number of digits is equal to 6, Therefore we check whether the given number is cyclic or not by multiplying it by 1, 2, 3, 4, 5, 6.

CYCLIC NUMBERS

ALGEBRA math facts Mathematicians Uncategorized

Is √2 irrational?

umasundresh 25 Aug 2022 No Comments

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.

ALGEBRA math facts

Pythagoras constant

umasundresh 18 Aug 2022 No Comments

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.

math facts Uncategorized

Honey bees and Hexagons

umasundresh 2 Aug 2022 No Comments

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

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.

Trending

Attoseconds

Like this:

Fictional Mathematicians

Like this:

Platonic Solids

1. Cube

2. Tetrahedron

3. Octahedron

4. Dodecahedron

5. Icosahedron

Like this:

Seconds in 6 weeks=10!

Like this:

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

Like this:

Applications of Logarithm in real life

Like this:

Cyclic Numbers

Like this:

Is √2 irrational?

Like this:

Pythagoras constant

Like this:

Honey bees and Hexagons

Like this:

You Missed

UV Index Formula Explained: What the Number on Your Weather App Really Means

Happy Pi Day 2026!

Amicable Numbers

Why Do Playing Cards Have 52 Cards?

2022

Share this:

Like this:

Share this:

Like this:

1. Cube

2. Tetrahedron

3. Octahedron

4. Dodecahedron

5. Icosahedron

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

Share this:

Like this:

You Missed