PurFact

Numbers & Constants

12 questions · Maths & Logic

Most numbers are simply numbers: but a few are so special that they have earned their own name, their own symbol and whole books full of stories. They turn up in the most unexpected places, from calculating a circle to your bank account to the patterns of nature, and some have fascinated mathematicians for thousands of years. This pack gathers the most famous numbers and constants: recognise the circle number Pi and Euler's number e, the golden ratio and the square root of 2, the imaginary unit i and the symbol for infinity, the enormous numbers googol and googolplex, the circle constant tau and the Euler (Mascheroni constant, as well as the two cornerstones of every calculation, zero and one) recognise them by their properties and discover why some of them are considered the most beautiful numbers in all of mathematics. Some of them link, in astonishing ways, fields that seem to have nothing to do with each other and that is exactly what still fascinates researchers today, and why some of these numbers even have devoted fans who memorise them to thousands of digits.

Practise for free

PurFact brings every card back right before you would forget it. That's how knowledge sticks.

All questions with answers

Which constant (≈ 3.14159) is the ratio of a circle's circumference to its diameter?

Show answer

Pi

Its decimals never end.

💡 Did you know? March 14 (3.14) is “Pi Day”.

Which constant (≈ 2.718) is the base of the natural logarithm?

Show answer

Euler's number

It describes natural growth and decay.

💡 Did you know? Like pi it is irrational and transcendental.

Which proportion (≈ 1.618) is seen as especially harmonious, the “divine proportion”?

Show answer

Golden ratio

It appears in art, architecture and nature.

💡 Did you know? It is closely tied to the Fibonacci sequence.

Which irrational number (≈ 1.414) multiplied by itself equals exactly 2?

Show answer

Square root of 2

It is the diagonal of the unit square.

💡 Did you know? Its irrationality shocked the ancient Greeks.

What is the number i, whose square is −1, called?

Show answer

Imaginary unit

It enables complex numbers.

💡 Did you know? No real number can do this.

Which symbol (∞) stands for a quantity without end?

Show answer

Infinity

The symbol is called a “lazy eight”.

💡 Did you know? There are even different sizes of infinity.

What is the number 10 to the power 100 (a 1 with a hundred zeros) called?

Show answer

Googol

It exceeds the number of atoms in the universe.

💡 Did you know? The search engine Google is named after it.

What is 10 to the power of (10 to the power of 100) called?

Show answer

Googolplex

It could never be fully written down.

💡 Did you know? It is unimaginably larger than a googol.

What is the circle constant τ, equal to twice pi (≈ 6.283), called?

Show answer

Tau

It is the ratio of circumference to radius.

💡 Did you know? Some find it more “natural” than pi.

What is γ (≈ 0.577), linking the logarithm and the harmonic series, called?

Show answer

Euler-Mascheroni constant

Whether it is rational is still unknown.

💡 Did you know? It is one of maths' great open questions.

Which number is the neutral element of addition?

Show answer

Zero

Adding zero changes nothing.

💡 Did you know? Inventing it as a number was a big step.

Which number is the neutral element of multiplication?

Show answer

One

Multiplying by one changes nothing.

💡 Did you know? It is not considered a prime.

How PurFact works

Practise for free

Maths & Logic: all topics →