Polygonal Hamster Wheel with 24901 sides.

[RaAmonKhan]

A Polygon hamster wheel has 24901 sides. Each side is made from a 1 mile long wooden plank(perfectly straight) , 4 feet wide. The planks are placed together, end to end, to form a giant hamster wheel.

You stand on top of this gigantic hamster wheel (on the outside of the wheel,as if balancing on a barrel), right where plank no.1 and plank no.2 meet each other in front of you. Behind you, a mile away ...plank no.24901 meets plank no.1 that you are standing on.

What would the angular difference be between each plank where they meet each other? Would you be able to see that angular difference with your eyes?

Riddle me that.

 

[HallsofIvy]

Imagine drawing lines from each "join" of two planks to the center of the wheel, There are 24901 planks so the entire 360 degrees is divided into 24901 angles each with measure \(\displaystyle \frac{360}{24901}\) degrees. Each angle is the vertex angle of an isosceles triangle. The sum of the angles in any triangle is 180 degrees so the base angles of each triangle have measure \(\displaystyle (180- \frac{360}{24901})/2= \frac{180(24901)- 360}{49802}= \frac{4481820}{49802}= 89.99277\). Since the "join" of two planks involves two of those, 2(89.99277)= 179.98 degrees. That is, of course, very very close to 180 degrees or no "angle" between planks at all. The difference from "straight" is 0.02 degrees. Whether you could "see that angular difference with your eyes would, I imagine, depend upon how good you eyesight is.

Exactly how big is this hamster?

 

[RaAmonKhan]

I wanted to see if it would be possible for the person (that is standing on this polygon circle of 24901 miles circumference) to perceive the round object it is standing on as "FLAT"...

Would you suggest this would be a possibility ?
So ...if at all...very very few people would be able to see the 0.02 degrees between the two 1 mile long perfectly straight sides..?

 

[RaAmonKhan]

The reason i am asking someone with much better math knowledge than myself this question..is to satisfy my reasoning about "why people perceive round objects of that size to be flat...when they are indeed round...or polygonal for testing purposes"
..
...The Earth is 24901 miles in circumference ...that is why some people perceive it to be "flat" ...when it is actually round.

Do i even make sense...sorry my English and grammar suck.Thank you for your input and valuable knowledge.

 

[RaAmonKhan]

Imagine drawing lines from each "join" of two planks to the center of the wheel, There are 24901 planks so the entire 360 degrees is divided into 24901 angles each with measure \(\displaystyle \frac{360}{24901}\) degrees. Each angle is the vertex angle of an isosceles triangle. The sum of the angles in any triangle is 180 degrees so the base angles of each triangle have measure \(\displaystyle (180- \frac{360}{24901})/2= \frac{180(24901)- 360}{49802}= \frac{4481820}{49802}= 89.99277\). Since the "join" of two planks involves two of those, 2(89.99277)= 179.98 degrees. That is, of course, very very close to 180 degrees or no "angle" between planks at all. The difference from "straight" is 0.02 degrees. Whether you could "see that angular difference with your eyes would, I imagine, depend upon how good you eyesight is.

Exactly how big is this hamster?

Forgot your question Sorry...the hamster is on average 5 feet in height.

 

[HallsofIvy]

Wow. Now I am going to worry about whether hamsters are vegetarian or carnivorous!