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A triangle is one of the basic shapes in geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted .
In Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space).
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients. It is named after the French mathematician Blaise Pascal in much of the Western world, although other mathematicians studied it centuries before him in India, Greece, Iran, China, Germany, and Italy.
The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top. The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. A simple construction of the triangle proceeds in the following manner. On row 0, write only the number 1. Then, to construct the elements of following rows, add the number above and to the left with the number above and to the right to find the new value. If either the number to the right or left is not present, substitute a zero in its place. For example, the first number in the first row is 0 + 1 = 1, whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.
In mathematics, Marden's theorem, named after Morris Marden but proven much earlier by Jörg Siebeck, gives a geometric relationship between the zeroes of a third-degree polynomial with complex coefficients and the zeroes of its derivative.
A cubic polynomial has three zeroes in the complex number plane, which in general form a triangle, and the Gauss–Lucas theorem states that the roots of its derivative lie within this triangle. Marden's theorem states their location within this triangle more precisely:
In journalism, a human interest story is a feature story that discusses a person or people in an emotional way. It presents people and their problems, concerns, or achievements in a way that brings about interest, sympathy or motivation in the reader or viewer.
Human interest stories may be "the story behind the story" about an event, organization, or otherwise faceless historical happening, such as about the life of an individual soldier during wartime, an interview with a survivor of a natural disaster, a random act of kindness or profile of someone known for a career achievement.