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**Pythagorean theorem** wiki / **Stelling van Pythagoras** (Dutch) wiki

In mathematics, the Pythagorean theorem, also known as Pythagoras’s theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the “Pythagorean equation”: a2 + b2 = c2 , where c represents the length of the hypotenuse and a and b the lengths of the triangle’s other two sides.

**47th problem of Euclid**

‘The proposition is especially important in architecture. Builders have since ancient times used the theorem in constructing buildings by a process known as “squaring a room.” As the theorem states that 3 squared + 4 squared = 5 squared, a builder starts by marking a spot and drawing a line, say line A. This line is given the value of 3. The builder then marks another point, say point B and draws a line from it at a right angle to line A, and it is given the value of 4. The distance between line A and B is then measured, and if the distance between A and B is 5, then the room is squared. By inverting the process, a “squared” (or rectangle) room can be obtained.

Engineers who tunnel from both sides through a mountain use the 47th problem to get the two shafts to meet in the center. The surveyor who wants to know how high a mountain may be ascertains the answer through the 47th problem. The astronomer who calculates the distance of the sun, the moon, the planets, and who fixes “the duration of times and seasons, years, and cycles,” depends upon the 47th problem for his results. The navigator traveling the trackless seas uses the 47th problem in determining his latitude, his longitude, and his true time. Eclipses are predicted, tides are specified as to height and time of occurrence, land is surveyed, roads run, shafts dug, bridges built, with the 47th problem to show the way.’

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