02/18/2024
RAMIFICATIONS OF PRIME NUMBERS IN GEOMETRY AND OTHERS
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this piece might sound as rambling since i did not right it on paper first. can there be a new branch that we PRIME PROGRAMMING.
initially there is linear programming where we try to optimize an objective function of many unknowns and satisfying linear constraints.
out of linear programming came INTEGER PROGRAMMING where the variables/unknowns in the problem are integers. after all you do not want the solution of a problem to come in the form of fraction of a car, two and half turbines, 3 and 1/9 ships and so on.
PRIME PROGRAMMING would solve problems where unknowns/variables that solve a system/optimize the objective function are prime numbers and others are rejected.
here is a simple situation: suppose there is a project that requires 17 tools, each will cost 43 (money/per day) for the duration of 23 days. the total cost is 17 x 43 x 23 = 16813. now this number 16813 would not come from any other way except from the 3 prime numbers involved.
similar wise if you have a square of material with side= 61 ( a prime number) and area will be 3721 square units, we will not be able to fully cut it into equal squares of any natural number side. (of course the special and trivial case of 61 unit square). so that square is not divisible.
similar a cube of side 71 (a prime). other than using 71^3 unit cubes, we can't totally fill it with other repeated cubes. it can only be filled with a cube of side = 71. i.e. it is indivisible to other repeated cubes.
the case of rectangular prism with the three sides represented with 3 different prime numbers is exactly like the first example given above of 17, 43, 23. again in this case you can't fill the prism with any repeated cubes (forget the repeated unit cubes), or any repeated rectangular prisms except for a prism of size 17, 43, 23..
i invite you to come up with more cases for PRIME PROGRAMMING for group discussion.
