Mathematical constant facts for kids

A mathematical constant is a special number that always stays the same. It has a fixed value that is important in math calculations. For example, the number π (pronounced "pie") is a mathematical constant. It tells us how many times a circle's width (its diameter) fits around its edge (its circumference). This value is always the same for any circle, big or small!

Unlike physical constants, which come from measuring things in the real world, mathematical constants come purely from mathematical ideas and rules.

What Are Mathematical Constants?

Mathematical constants are numbers that show up often in different areas of math and science. They are usually represented by special symbols, like π or e. These numbers help us understand patterns and relationships in the world around us.

Types of Constants

Mathematical constants can be different types of numbers:

• Rational numbers (R): These can be written as a simple fraction, like 1/2 or 3/4.
• Irrational numbers (I): These cannot be written as a simple fraction. Their decimal forms go on forever without repeating, like the square root of 2.
• Transcendental numbers (T): These are a special kind of irrational number. They are not the root of any non-zero polynomial equation with integer coefficients. This means they can't be found by solving simple algebra problems. Pi (π) and e are examples of these.
• Complex numbers (C): These numbers include a "real" part and an "imaginary" part. An example is i, which is the square root of -1.

Important Mathematical Constants

Here are some of the most famous and important mathematical constants:

Name	Symbol	Value (approximate)	What it means
Pi, Archimedes' constant	π	≈3.14159	This number shows the relationship between a circle's edge (circumference) and its width (diameter). It's also used to find the area of a circle.
E, Napier's constant	e	≈2.71828	This number is super important in math for things like natural growth and decay, and it's the base for natural logarithms.
Golden ratio	φ	≈1.618	This special ratio appears in nature, art, and architecture. It's found when a line is divided into two parts so that the whole length divided by the longer part is equal to the longer part divided by the shorter part.
Square root of 2, Pythagoras' constant		≈1.414	This irrational number is the length of the diagonal of a square if its sides are 1 unit long. It cannot be written as a simple fraction.

Images for kids

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  The circumference of a circle with diameter 1 is π.

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  Bifurcation diagram of the logistic map, which shows how complex systems can change.

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  The area between these two curves (red) gets closer to a special number called the Euler-Mascheroni constant.

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  This ancient Babylonian clay tablet shows a very old way of estimating the square root of 2.

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  These lines show different solutions to a math problem, each with a different "constant of integration."

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  The square root of 2.

See also

In Spanish: Constante (matemática) para niños