Problem 45408. Yoonir - 03

Created by Asif Newaz

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; "><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 215.5px 8px; transform-origin: 215.5px 8px; unicode-bidi: normal; "><span style="">Find the area of a seven-pointed star inscribed in a circle of radius r.</span></span></div></div></div>

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38 Solutions
16 Solvers

Last Solution submitted on Feb 20, 2023

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6 Comments

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William on 5 Apr 2020

Hi Asif,
I'm puzzled. Now 2 people have submitted solutions that agree with the test suite, but the test suite seems wrong to me! Looking at all 3 'yoonir' problems for a radius of 10 units:
Program Points test_suite my_calc
yoonir_02 5 112.27 112.26
yoonir_04 6 173.20 173.21
yoonir_06 7 108.34 210.17
How would it be possible that in going from a 6 pointed star to a 7 pointed star, the area drops from 173.2 to 108.3?

Asif Newaz on 7 Apr 2020

hello William,

in the figure, the available area inside the polygon of a 7-pointed star has actually decreased compared to 6-pointed star .isn't it?

Asif Newaz on 7 Apr 2020

https://i.pinimg.com/474x/27/ce/d6/27ced6447ff40b38ae3d5784b30936a9.jpg

William on 7 Apr 2020

Gosh, that seems to be right! I thought my solution was good for all N, but I can see from that figure that it's not. Thanks for the tip.

William on 8 Apr 2020

Asif,
I have discovered something! While there is just one way to draw a five-pointed star or a six-pointed star, there are actually two ways to draw a seven-pointed star. One of them has an area much larger than the other.

Asif Newaz on 9 Apr 2020

yes i saw that later on utube..didn't know that before

Solution Comments

Solution 2185339

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1 Comment

Asif Newaz on 2 Apr 2020

It was actually unintentional. I originally intended to submit only the 1st problem of yoonir(which is a 5 pointed star) but then it suddenly came to mind what about a 6/7 pointed star. Tried to calculate one by one.

a generalized problem of an n-pointed star would have been gd.

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Problem 45408. Yoonir - 03

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Problem 45408. Yoonir - 03

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