Portal:Mathematics
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Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. (Full article...)
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- ... that in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
- ... that multiple mathematics competitions have made use of Sophie Germain's identity?
- ... that Kit Nascimento, a spokesperson for the government of Guyana during the aftermath of Jonestown, disagrees with current proposals to open the former Jonestown site as a tourist attraction?
- ... that the identity of Cleo, who provided online answers to complex mathematics problems without showing any work, was revealed over a decade later in 2025?
- ... that in the aftermath of the American Civil War, the only Black-led organization providing teachers to formerly enslaved people was the African Civilization Society?
- ... that the British National Hospital Service Reserve trained volunteers to carry out first aid in the aftermath of a nuclear or chemical attack?
- ... that mathematician Daniel Larsen was the youngest contributor to the New York Times crossword puzzle?
- ... that Fathimath Dheema Ali is the first Olympic qualifier from the Maldives?
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- ...that in a group of 23 people, there is a more than 50% chance that two people share a birthday?
- ...that the 1966 publication disproving Euler's sum of powers conjecture, proposed nearly 200 years earlier, consisted of only two sentences?
- ...the hyperbolic trigonometric functions of the natural logarithm can be represented by rational algebraic fractions?
- ... that economists blame market failures on non-convexity?
- ... that, according to the pizza theorem, a circular pizza that is sliced off-center into eight equal-angled wedges can still be divided equally between two people?
- ... that the clique problem of programming a computer to find complete subgraphs in an undirected graph was first studied as a way to find groups of people who all know each other in social networks?
- ... that the Herschel graph is the smallest possible polyhedral graph that does not have a Hamiltonian cycle?
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All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Image credit: User:Tttrung |
The trigonometric functions are functions of an angle; they are most important when studying triangles and modeling periodic phenomena, among many other applications. They are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to positive and negative values and even to complex numbers.
The study of trigonometric functions dates back to Babylonian times, and a considerable amount of fundamental work was done by ancient Greek, Indian and Arab mathematicians. (Full article...)
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