Squarcles Estimates, plausibility arguments polynomial and exponential growth Recall the "activity" involving connecting N points on a squircle x' + y = 1 + - 1 and forming regions (a.k.a. components ). Provide a self-contained explanation of the activity, in your own words. Discuss early resulting examples. Why might one want to start illustrating with three points? Why not start with two, or one (or even zero) points? In class we discussed the trend in the number of regions generated, made argu- ments and estimates, and drew conclusions. There was some handwaving, but it was not visible, since the video camera was off. (There was no jawboning.) Interpret and rewrite the a priori plausibility arguments given in class, pur- portedly showing that the exponential growth in the number of components is -unsustainable'. Be sure to define all appropriate terms, such as edge, secant or chord, node, exponential growth, etc. You need not define terms exactly as done in class; however, your writing should be self-contained; definitions should be consistent and workable and should lead to sound analysis. You may discuss the ideas of the argument with others; however, the final writ- ing should be composed from scratch by you alone. Indicate clearly any outside sources you use and explain fully all results not coming from within class re- sources. The assignment should be no longer than what would fit on a single sheet of paper (2-sided). Instructions for BlackBoard (Bb) upload will be pro- vided. what does a priori mean and how is it used in a mathematical context'] [Ed.: hand-waving noun the use of gestures and insubstantial language meant to impress or convince: their patriotic hand-waving lacked sincerity Iros modifier her path of logic and hand-waving explanations jawbone 10 bon noun a bore of the jaw, especially that of the lower jaw (the mandible), ore/ther half of this verb (with object North American informal attempt to persuade or pressure by the force of one's position of authority the Federal Reserve Board Vice Chairman jawboned the dollar higher by calling its recent steep decline a purely speculative phenomenon object an analyst woning about the industry Squarcles Estimates, plausibility arguments polynomial and exponential growth Recall the "activity" involving connecting N points on a squircle x' + y = 1 + - 1 and forming regions (a.k.a. components ). Provide a self-contained explanation of the activity, in your own words. Discuss early resulting examples. Why might one want to start illustrating with three points? Why not start with two, or one (or even zero) points? In class we discussed the trend in the number of regions generated, made argu- ments and estimates, and drew conclusions. There was some handwaving, but it was not visible, since the video camera was off. (There was no jawboning.) Interpret and rewrite the a priori plausibility arguments given in class, pur- portedly showing that the exponential growth in the number of components is -unsustainable'. Be sure to define all appropriate terms, such as edge, secant or chord, node, exponential growth, etc. You need not define terms exactly as done in class; however, your writing should be self-contained; definitions should be consistent and workable and should lead to sound analysis. You may discuss the ideas of the argument with others; however, the final writ- ing should be composed from scratch by you alone. Indicate clearly any outside sources you use and explain fully all results not coming from within class re- sources. The assignment should be no longer than what would fit on a single sheet of paper (2-sided). Instructions for BlackBoard (Bb) upload will be pro- vided. what does a priori mean and how is it used in a mathematical context'] [Ed.: hand-waving noun the use of gestures and insubstantial language meant to impress or convince: their patriotic hand-waving lacked sincerity Iros modifier her path of logic and hand-waving explanations jawbone 10 bon noun a bore of the jaw, especially that of the lower jaw (the mandible), ore/ther half of this verb (with object North American informal attempt to persuade or pressure by the force of one's position of authority the Federal Reserve Board Vice Chairman jawboned the dollar higher by calling its recent steep decline a purely speculative phenomenon object an analyst woning about the industry
