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Baker’s Dozen: Why 13 Instead of 12?

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In math, we know that a dozen means 12. But have you heard of a baker’s dozen? It means 13 instead of 12! This tradition started long ago in medieval England.

Back then, there were strict rules about the weight of bread. If a baker sold loaves that were too light, they could be fined or punished. To be safe, bakers started giving one extra loaf when selling a dozen. That way, even if some loaves were slightly smaller, customers always got their full weight of bread. Over time, this became known as the baker’s dozen—13 instead of 12.

Baker’s Dozen

Happy Learning!!!

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Pi (⌅) Day!!!

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Earnmath wishes you all a very happy International pi day!!!

Pi day!!!

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Are there only 64 squares present on the chess board?

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This is a trick question because it is possible for someone to get confused and immediately calculate the total number of squares in a chessboard with eight rows and eight columns by using the formula (number of rows X number of columns)

= 8 X 8 = 64.

Let’s start by reducing the complexity of the situation.

The total number of 1X1 squares is presented in eight rows by eight columns on the chess board.

= 8 X 8 =64.

However, if you start thinking about 2X2 squares, 3X3 squares, and so on up to 8X8 squares, you can figure out how to answer the question.

The total number of 2X2 squares is presented in seven rows by seven columns on the chess board.

= 7 X 7 =49.

The total number of 3X3 squares is presented in six rows by six columns on the chess board.

= 6 X 6 =36.

The total number of 4X4 squares is presented in five rows by five columns on the chess board.

= 5 X 5 =25.

The total number of 5X5 squares is presented in four rows by four columns on the chess board.

= 4 X 4 = 16.

The total number of 6X6 squares is presented in three rows by three columns on the chess board.

= 3 X 3 = 9.

The total number of 7X7 squares is presented in two rows by two columns on the chess board.

= 2 X 2 = 4.

The total number of 8X8 squares is presented in one row by one column on the chess board.

= 1 X 1 = 1.

Therefore, the total number of squares presented on the chess board is found by summing up all the values obtained by 1X1, 2X2, 3X3, 4X4, 5X5,6X6,7X7 and 8X8 squares.

i.e., 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204.

Therefore, the total number of squares on the chess board is 204.

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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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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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THALES

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Thales used the principles of geometry to solve real life problems. Therefore, he is considered as the ‘First true mathematician’.

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DICE FACT

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The opposite sides of a dice always add up to seven.
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SURREAL NUMBERS

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These are the elements of a huge set of numbers that includes all real numbers as well as infinite numbers and infinitesimal numbers.

* Infinite numbers: Larger in value than any positive integer

*Infinitesimal numbers: Smaller than any positive real number.

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HISTORY OF QUATERNIONS

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The irish mathematician  William Rowan Hamilton discovered quaternions.

Now it is used in the areas related to 3d geometry like computer games, spaceship navigation etc.,

  • William always has the thought that numbers consists of three parts.(in the manner that complex number consists of 2 parts a+ib.
  • While he was walking along Royal canal in Dublin he felt that the number he was searching was 4 parts.
  • He was so happy with his discovery and he carved the basic formula on one of the bridges over the canal.
  • A quaternion is a number can be written as a+bi+cj+dk , where a, b , c, d are real. and i,j, k has the following properties.

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Quaternions

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Quaternions have the property that ‘x’ multiplied by ‘y’ is not equal to ‘y’ multiplied by ‘x’. These quaternions are used today in the areas related to 3 dimensional geometry.

we see its brief history in my next blog.

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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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Geometry Math around us math facts Math titbits

Happy Pi Day 2026!