ABSTRACT
In this Study, the solution of optimization problems is considered with reference to the problems of the reflection and of the refraction of light. A numerical and analytical solution of the algebraic equations of a lens and a focussing mirror are presented. It is shown how modern software can easily and elegantly solve optical problems. The optical property of the hyperbola, based not on the law of reflection, but on the law of refraction of light, is emphasized.
Mathematics: Solution of the equation, optimization, plane curves of the second order, Fermat’s theorem.
Physics: Distance, time, speed, geometric optics, refraction and reflection of light, the Fermat principle, the principle of tautochronism, the optical path of a light beam.
IT: Numerical solution of an optimization problem, numerical solution of an algebraic equation, computer tools for analytical transformations (symbolic mathematics), computer graphics of planar curves, embedded cycle with parameter.
Art: Daniil Kharms, “Holiday”; Aleksey Nikolayevich Tolstoy, The Hyperboloid of Engineer Garin.
Study website: https://community.ptc.com/t5/PTC-Mathcad-Questions/Study-20/m-p/566163" xmlns:xlink="https://www.w3.org/1999/xlink">https://community.ptc.com/t5/PTC-Mathcad-Questions/Study-20/m-p/566163
The janitor nailed the flag to the house.
The passer-by asked what it meant.
The janitor answered: “This means that there is a holiday in the city.”
“And what is this holiday?” asked the passer-by.
“There is a holiday because our mathematician has found one more optical property of hyperbola!” answered the janitor.
The passerby, embarrassed by his ignorance, dissolved into the air.
Daniil Kharms “Holiday” (new edition) https://en.wikipedia.org/wiki/Daniil_Kharms" xmlns:xlink="https://www.w3.org/1999/xlink">https://en.wikipedia.org/wiki/Daniil_Kharms
