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The Pythagoreans helped to develop formulas after looking at data collected from their observations.  Their most famous observation is the Pythagorean Theorem.  This theorem states that for a right angle triangle the square of the hypotenuse is equal to the sum of the squares on the other sides (a2 + b2 = c2).  Click on picture for animation to see a visual proof of the theorem.  This also led to an understanding of irrational numbers.  Pythagoreans also developed an understanding of geometrical algebra.

Math models the world.  If you look at the world differently you get different models.  Geometry, for example, deals with deduction of properties, measurements, and relationships of points, lines, angles, and figures in space.  Euclidean geometry deals with a flat world that states that parallel lines are always parallel and never intersect.  Euclidean geometry is our way of measuring on Earth.  On the other hand, Riemannian geometry deals with a spherical world that says parallel lines will intersect.  This takes into consideration, the Universe may be a closed surface.

 Euclid Bernhard Riemann (1826-66)
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