If you can recall it, do you remember the math problem in question? And could you loosely explain how you transformed it?(just with general concepts or keywords for my own curiosity. I love math, and seeing how different problems can relate to each other in unexpected ways. For example, when the sum of two quadratic roots gives the width of a given rectangle. Like this problem: A rectangle has an area of 32ft² . Its width is 4ft less than its length. What is the width? A = l(w) and 32 = l(l - 4). I’ll spare you the work shown, but l = 8 and l = -4. … (8) + (-4) = 4 = w
Roughly it can be viewed as a change of coordinates and then recognizing the symmetry. Say you had a 2D function of x and y and transformed it to r and theta and then noticed that it was independent of theta. You go from an 2D problem to a 1D one.
In this case we’re transforming a 7D problem into a sum of a discrete set of 2D problems. With more algebra we could get it down to a 1D problem but that would take more human work that wouldn’t be paid off later in CPU time. If their project ends up scaling and the 1D transformation makes sense, we’ll do it.
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If you can recall it, do you remember the math problem in question? And could you loosely explain how you transformed it?(just with general concepts or keywords for my own curiosity. I love math, and seeing how different problems can relate to each other in unexpected ways. For example, when the sum of two quadratic roots gives the width of a given rectangle. Like this problem: A rectangle has an area of 32ft² . Its width is 4ft less than its length. What is the width? A = l(w) and 32 = l(l - 4). I’ll spare you the work shown, but l = 8 and l = -4. … (8) + (-4) = 4 = w
Roughly it can be viewed as a change of coordinates and then recognizing the symmetry. Say you had a 2D function of x and y and transformed it to r and theta and then noticed that it was independent of theta. You go from an 2D problem to a 1D one.
In this case we’re transforming a 7D problem into a sum of a discrete set of 2D problems. With more algebra we could get it down to a 1D problem but that would take more human work that wouldn’t be paid off later in CPU time. If their project ends up scaling and the 1D transformation makes sense, we’ll do it.
What field of mathematics is this?