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Pi

π (or pi) is a mathematical constant that is the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159. π is an irrational number, which means that it cannot be expressed exactly as a ratio of two integers, although it is roughly approximated by 22/7. It is a transcendental number – a number that cannot be produced with a finite sequence of algebraic operations (sums, products, powers, and roots). The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and ruler. The digits in the decimal representation of π appear to be random. Because its definition relates to the circle, π is found in many formulae in trigonometry and geometry, such as Euler's identity, e + 1 = 0. It is also found in formulae from other branches of science, such as cosmology, number theory, statistics, fractals, thermodynamics, mechanics, and electromagnetism. (more...)

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July 22: Feast day of Mary Magdalene; Parents' Day in the United States (2012); Pi Approximation Day

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Simulated depth of field

A 3D ray tracing of a glass molecular model, demonstrating the algorithm's ability in simulating depth of field (DOF), which is the distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image. When much of the foreground and background of an image is sharp, its DOF is deep. The opposite is called shallow focus.

Image: Purpy Pupple

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