A polar graph is just a normal graph with its x-axis wrapped around a point.

1 + 1/2 + 1/3 + 1/4 + … grows without bound, but extremely slowly. After 10 terms, the sum is 2.93. To exceed 10, you need 12,367 terms; to exceed 20, about 272 million terms; and to exceed 100, about 1.5 × 10⁴³ terms!

A repunit is a number written entirely with ones. Square one, and the result reads the same forwards and backwards. The pattern holds only up to nine ones. With ten, the middle column sums to 10, carrying begins, and the symmetry breaks.

1 - 1/2 + 1/4 - 1/8 + ... = 2/3

The decimal expansion of 1/998001.

Transforming the Riemann sum into a definite integral: 👇

How people make the square root symbol.

Circle, ellipse, parabola and hyperbola are all slices of the same double cone; only the angle of the plane differs.

Remembering Homi Jehangir Bhabha (1909–1966) on his 117th birth anniversary. Physicist, institution-builder, and architect of India’s nuclear programme. He founded TIFR and the Trombay establishment that now bears his name: BARC.

Here is a portrait of Euclid, who is known as the "Father of Geometry"! No one actually knows what he looked like. No authentic statue, painting, or physical description of him exists. Any depictions of him are purely products of the artist's imagination.

Set Theory Symbols.

Some Important Notations in Calculus.

The Feynman point, named after the physicist Richard Feynman, is a famous mathematical coincidence: a sequence of six consecutive 9s in the decimal representation of π, starting at the 762nd decimal place.

It's impossible for mathematics to be ugly.

An arrow that refuses to turn. Designed by mathematician Kokichi Sugihara. It points in the same direction even after a 180° rotation. The object is identical to itself after a half-turn, while its curved edges trick the brain into seeing an arrow.

Illustration of the irrationality of π. Two arms rotate, one π times as fast as the other. If π were a ratio of two whole numbers, both arms would eventually realign and the curve would close. Since π is irrational, the curve never closes and never repeats.

You are free to choose who you want to be.

Maxwell–Boltzmann distribution. The air around you is full of tiny molecules, and at room temperature most of them move faster than the speed of sound. They do not all move at the same speed. A few are slow, most cluster around a typical speed, and a rare few are extremely fast. In 1860, James Clerk Maxwell worked out how these speeds are distributed. Ludwig Boltzmann later extended the idea. Here 1,200 beads play the molecules. The faster a bead flies out, the farther it lands, so each slot collects beads of similar speed. Together, the piles trace the Maxwell–Boltzmann curve.