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An inscribed angle is an angle ∠ABC formed by points A, B, and C on a circle's circumference as illustrated above. For an inscribed angle ∠ABC and central angle ∠AOC with the ...

Interest is a fee (or payment) made for the borrowing (or lending) of money. The two most common types of interest are simple interest, for which interest is paid only on the ...

The illusion shown above which was discovered by Helmholtz in the 19th century. Despite the fact that the two above figures are identical in size, the white hole looks bigger ...

Given a point P in the interior of a triangle DeltaA_1A_2A_3, draw the cevians through P from each polygon vertex which meet the opposite sides at P_1, P_2, and P_3. Now, ...

The Kenmotu circle is the circle passing through the six contact points of the congruent squares used in the construction of the Kenmotu point with the triangle sides. It is ...

Let S={x_1,...,x_n} be a set of n distinct positive integers. Then the matrix [S]_n having the least common multiple LCM(x_i,x_j) of x_i and x_j as its i,jth entry is called ...

Given a point P and a line AB, draw the perpendicular through P and call it PC. Let PD be any other line from P which meets CB in D. In a hyperbolic geometry, as D moves off ...

The middle levels conjecture, also known as revolving door conjecture, posits that the middle layer graph has a Hamilton cycle for every n>=1. The conjecture was proved by ...

Pathological functions that are continuous but differentiable only on a set of points of measure zero are sometimes known as monsters of real analysis. Examples include the ...

Multi-index notation is used to shorten expressions that contain many indices. Let x in R^n and write x=(x_1,...,x_n). A multi-index alpha is an n-tuple of integers alpha_j ...