Page - 46 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

46 2 BasicConstructions Thevertices (“corners”) of the polygonhave coordinates .x1;y1/, .x2;y2/, : : :, .xn;yn/, numberedeither in a clockwiseor counter clockwise fashion. TheareaA of the polygoncan amazingly be computedby just knowing the boundary coordi- nates: AD 1 2 j.x1y2Cx2y3C Cxn 1ynCxny1/ .y1x2Cy2x3C Cyn 1xnCynx1/j : Write a functionpolyarea(x, y) that takes two coordinate arrayswith the ver- tices as arguments and returns the area. Assume that x and y are either lists or arrays. Test the function on a triangle, a quadrilateral, and a pentagonwhere you can calculate theareabyalternativemethods forcomparison. Hint SincePython lists andarrayshas0as theirfirst index, it iswise to rewrite the mathematical formula in termsofvertex coordinatesnumberedasx0;x1;:: :;xn 1 andy0;y1;:: :;yn 1. Filename:polyarea.py. Exercise2.6:Averageof integers Writeaprogramthatgetsan integerN >1 fromtheuserandcomputes theaverage of all integers i D 1;:: :;N . The computation should be done in a function that takesN as input parameter. Print the result to the screenwith an appropriate text. Run theprogramwithN D5andconfirmthatyouget thecorrectanswer. Filename:average_1_to_N.py.