Every polygon can be built from triangles. Trigonometry means "measuring triangles". It originated in astronomy, where it was easy to measure angles but it was very difficult to measure the vast distances. The first trigonometric tables were derived by Hipparchus around 150 BC.
In Astronomy the natural sphere to work in was not the plane but the sphere. So the astronomical calculations refer to the geometry of a sphere, not that of a plane. If two triangles have the same angles as each other, then they are congruent (having the same size and shape).
The Almagest meaning the greatest, featured how it handled the orbits of the planets. Appolonius used epicycles to represent the complex motions in terms of revolving spheres mounted on other spheres, where the circles where those whose centers moves along other circles and so on.
George Joachim Rhaeticus stated the law of sines for spherical triangles and the law of cosines.
Logarithms importance is that they satisfies the equation and can therefore be used to convert multiplications into additions.
I had a big insight reading this chapter because today we were reading about Self Reliance from Ralph Waldo Emerson, and we discussed the importance of speaking your ideas and not be afraid of failure. The piece of work that shocked me was that the history of mathematicians depended on what people publish and made public for others to benefit from, but the ideas that remain private are the ones that it had no influence on anyone else.
Trigonometry has influenced our life very significantly, in the use of map and in commerce, and in a lot of more other advances.
In Astronomy the natural sphere to work in was not the plane but the sphere. So the astronomical calculations refer to the geometry of a sphere, not that of a plane. If two triangles have the same angles as each other, then they are congruent (having the same size and shape).
The Almagest meaning the greatest, featured how it handled the orbits of the planets. Appolonius used epicycles to represent the complex motions in terms of revolving spheres mounted on other spheres, where the circles where those whose centers moves along other circles and so on.
George Joachim Rhaeticus stated the law of sines for spherical triangles and the law of cosines.
Logarithms importance is that they satisfies the equation and can therefore be used to convert multiplications into additions.
I had a big insight reading this chapter because today we were reading about Self Reliance from Ralph Waldo Emerson, and we discussed the importance of speaking your ideas and not be afraid of failure. The piece of work that shocked me was that the history of mathematicians depended on what people publish and made public for others to benefit from, but the ideas that remain private are the ones that it had no influence on anyone else.
Trigonometry has influenced our life very significantly, in the use of map and in commerce, and in a lot of more other advances.