The intercept theorem, also known as Thales' theorem (not to be confused with another theorem with that name), is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels.

De Bruijn–Erdős theorem (incidence geometry)

In incidence geometry, the De Bruijn–Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős (), states a lower bound on the number of lines determined by n points in a projective plane.

Ellipse

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

Hyperbola

In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

Arc (geometry)

In Euclidean geometry, an arc (symbol: ⌒) is a closed segment of a differentiable curve.

Median (geometry)

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side.

Doubling the cube

Doubling the cube, also known as the Delian problem, is an ancient geometric problem.

Pole and polar

In geometry, the pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given conic section.

Wittgenstein's rod

Wittgenstein's rod is a geometry problem discussed by 20th century philosopher Ludwig Wittgenstein.

Disquisitiones Arithmeticae

The Disquisitiones Arithmeticae (Latin for "Arithmetical Investigations") is a textbook of number theory written in Latin by Carl Friedrich Gauss in 1798 when Gauss was 21 and first published in 1801 when he was 24.