Mathcad polyroots function11/13/2022 Another quick and elegant solution (very few functions involved), finished off with a plot of the combined area as a function of the diameter to verify a correct solution. Therefore, he expressed the length of the side of the square in terms of the circle’s diameter defined functions for the areas of the circle, square, and combined area and used the root function to solve for the diameter. User “Werner_E” remarked that he could not use symbolic evaluation due to using Mathcad Express. My only quibble is that by solving for the radius instead of the diameter, they missed out on the revelation that the diameter of the circle and the length of a side of the square are equal. Then they used the derivative operator, symbolic evaluation with the coeffs keyword, and the polyroots function. They set up user-defined functions for the perimeter and area calculations in terms of a single variable, the circle radius. They recognized that one method of finding a maximum or minimum is by evaluating the roots of the first derivative of a function. The second entry by user “ppal” took a slightly different approach. To confirm the validity of the solution, he used a program and functions to graph the areas versus inputs on an XY Plot. He entered his guess values, constraints, and vector to be minimized. The Solve Block construct is my favorite tool in Mathcad because of its beauty. Terry used a Solve Block, which is the approach that immediately came to my mind for solving the problem. Once again, Terry was the first to respond, less than 10 hours after the challenge was posted. Let’s take a look at what makes each of the submissions special. Once again, if you have not looked at the solutions that people submitted, I strongly encourage you to do so. What tools within Mathcad can provide you with a result? Optional: How can you depict the results? Can you use a 2D plot or Chart Component to visualize the answer? This month’s Mathcad Community Challenge asked users to solve an isoperimetric problem:Ĭreate a worksheet in which you calculate (1) the diameter of a circle and (2) the length of a side of a square that yields the minimum combined area for a combined perimeter of 1 meter.
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