Zero is relatively new! Although mathematics has been around for thousands of years, the concept of zero as a number was not used until about the 5th century CE in India. It was later transmitted to Europe via Arabic mathematics.
Infinity has sizes! Not all infinities are equal. For example, the set of real numbers is a “larger” infinity than the set of natural numbers. This was shown by mathematician Georg Cantor, introducing the concept of countable and uncountable infinities.
The golden ratio is everywhere! Approximately equal to 1.618, the golden ratio appears in art, architecture, nature (like sunflower spirals), and even in financial markets. It’s denoted by the Greek letter φ (phi).
A perfect number is equal to the sum of its divisors (excluding itself) For example, 28 is a perfect number because: 1 + 2 + 4 + 7 + 14 = 28.
Pi (π) never ends or repeats Pi, the ratio of a circle’s circumference to its diameter, is irrational, meaning it has an infinite number of non-repeating digits. Computers have calculated trillions of digits of π.
Mathematics can describe music Harmonics, frequencies, and rhythms can all be described using mathematical ratios and patterns. For instance, a musical octave doubles the frequency of a note.
You can “hear” the shape of a drum This refers to a famous question in mathematics: Can one hear the shape of a drum? It explores how the sound frequencies of a shape relate to its geometry—a deep connection between math and physics.
A Möbius strip has only one side If you take a strip of paper, give it a half-twist, and tape the ends together, you create a Möbius strip. It has just one surface and one edge—a famous object in topology.
The Fibonacci sequence appears in nature The sequence (0, 1, 1, 2, 3, 5, 8…) is found in natural patterns like pinecones, flower petals, and hurricanes.
The four-color theorem It states that any map drawn on a plane can be colored with just four colors so that no two adjacent regions share the same color. This was one of the first major theorems proven using a computer.
