10 most difficult geometry riddles

Gaspard Monge was a French mathematician, the inventor of descriptive geometry, and the father of differential geometry. During the French Revolution he served as the Minister of the Marine, and was involved in the reform of the French educational system, helping to found the École Polytechnique.

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity.The word asymptote is derived from the Greek which means "not falling together".

In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle. Equivalently, it is a non-convex plane region bounded by one 180-degree circular arc and one 90-degree circular arc. It is the first curved figure to have its exact area calculated mathematically.

Lemniscate refers not only to the infinity symbol, but also to any geometric shape that is curved like a figure-eight.

The minute hand makes 24 revolutions, while the hour hand makes 2 revolutions.

For each circle, the length of the circumference is c=2πr. Hence, if a radius grows by 1 meter, the circumference grows by 2 π meters - no matter what the initial value of radius was.

Continuous travel North must eventually end at the North Pole. So, the maximum distance is half of the Earth's meridional circumference, which can be reached if a plane starts at the South Pole.

Pentagramma mirificum (Latin for miraculous pentagram) is a star polygon on a sphere, composed of five great circle arcs, whose all internal angles are right angles. This shape was described by John Napier in his 1614 book along with rules that link the values of trigonometric functions of five parts of a right spherical triangle (two angles and three sides). The properties of pentagramma mirificum were studied, among others, by Carl Friedrich Gauss.

In geometry, the spiral of Theodorus is a spiral composed of contiguous right triangles. It was first constructed by Theodorus of Cyrene.The principle of construction is based on the Pythagorean theorem.

The letter "i" as a designation of the element from -1 was proposed by Leonhard Euler in 1777. Later, from 1801, this designation was popularized by Carl Friedrich Gauss. Currently, it is the most commonly used symbol of the imaginary unit.