Abstract
Getting to 3D has required several steps, which were not a logical process done with an end goal in mind. Rather it was the natural outcome of one discovery leading to another, but driven by intellectual curiosity, genius, and occasionally chance discovery. When tracing the history of anything there has to be time and basic distance measurement. From that, we trace the development of basic geometry, and find that the triangle is foundation of all computer graphics. Even before triangles, we had to be able to count, and the first numbering systems date back to 5000 BCE. A system of numbers requires rules, rules that will support predictability and repeatability. In India, Panini established the Sanskrit grammar, and the grammar known as Ashtadhyayi, which was beginning of linguistics. That was necessary so we could share our counting and designs with other people. Thales of Miletos brought the science of geometry from Egypt to Greece, three centuries before Euclid. Pythagoras known for the Pythagorean Theorem used those concepts. After Thales introduced deductive reasoning in the 300s BCE, Euclid organized the teachings of Pythagoras into his own great work, The Elements. Then we had to learn how to use zero, and from there negative numbers, on to matrix math and transformations. It took close to 6,000 years to get to the point where we understood 2D geometry. The next step was to extend it to 3D. That wasn’t as easy as it sounds and Heron of Alexandria, mastered it in Egypt in the first century.
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Notes
- 1.
In linear algebra, Gaussian elimination is an algorithm used to determine the solutions of a system of linear equations, to find the rank of a matrix, and to calculate the inverse of an invertible square matrix, named after the German mathematician and scientist Carl Friedrich Gauss.
- 2.
In geometry, the semiperimeter of a polygon is half its perimeter.
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Appendix
Appendix
2.1.1 Math History
http://www.storyofmathematics.com/indian.html
http://www.math.wichita.edu/history/topics/num-sys.html
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Peddie, J. (2013). Getting to 3D. In: The History of Visual Magic in Computers. Springer, London. https://doi.org/10.1007/978-1-4471-4932-3_2
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