Centroid of figure between two circles

chaffeur shared this question 7 years ago

Answered

Hi,

I'ld like to find what said in title by using the command Centroid [<Polygon>] being the polygon constructed through lists of points embedding the figure border via slider. Calculus gives the shown G position. Thanks and Regards

Philippe

https://ggbm.at/562189 da2bd7e55154b7f7232bbea1b16cbfd1

Files: 01.png

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Comments (4)

chaffeur ● 7 years ago

Good drift, Noel!

My idea is better described in the figure. Both lists should be embedde in one, so that the unique command Centroid[Polygon] will converge, by increasing the sides n, into the value computed with circle. In other words, with few sides the computed point is far from the one coming from exact calculations.

Thanks&Regards

Philippe 10f63579038cf9a52acdc497c9e90e34

Files: 11.png

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chaffeur ● 7 years ago

...but I find it hard to talk of "convergence" ....

What I mean as centroid convergence is shown below. Point A (centroid) with few sides is quite discrepant to more accurate one (n=19). The main difficulty for me resides on defining (via slider) the path of the voided figure regarding the second circle. Regards

Philippe 594fb006347daa2081ba229b39f0fabe

Files: centroid-A.png

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mathmagic ● 7 years ago

hello

ok,Noel

hey chaffeur, if you want a no constant serie you need no regular polygons or different number of sides, ie: n sides for small polygon and n+2 sides for big polygon

or n and 2n

saludos

PS: perhaps better with semicircles

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chaffeur ● 7 years ago

Interesting result reached by Noel's construction: the centroid invariance with any polygon sides, as shown below.

It could be an ... assist for theoretical demonstations. Regards and compliments, Noel.

Philippe

PS: by activating the animation, see the position of centroid G, always there!

https://ggbm.at/562217 e4a88f9f77b9e345635e0d37acf460bb

Files: 13.png

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