Question

given a tennis ball with radius r
what may be the way to calcule the length of the line from the surface of this ball ?

Answer 1

any idea ? thank you in advance

Answer 2

@Hero
@Vocaloid

please

Answer 3

Woah! That's a huge tennis ball. I didn't really get what you were asking though.


So that white line lies on the surface area of the spherical ball. Are trying to find the distance between the line and the center of the sphere?

Answer 4

I think I get what you mean. You're trying to find the length of the white line?

Answer 5

Here's what I suggest:

First draw 4 diagrams from each view of the ball, because once you do that, then you'll understand how to find the total length of the white seam. On each circle there should be several semi circles. You would find their circumferences, then add it up.

Answer 6

Let me see if there's a diagram similar to what I'm trying to say.

Answer 7

I'm not sure how else to do it unless there's more information.

Answer 8

@Ferredoxin4 this is a very nice idea ... on what more informations do you think ?

Answer 9

I thought of another nice idea..let me first draw it out.

Basically use a net for a sphere and draw out the seam on that net. Then you can calculate the length in a much easier, 2D way.

Answer 10

@Ferredoxin4 i wait your help - thank you in advance

Answer 11

Oh sorry, ill draw it out and send it to you when i get a chance. Ty for your patience

Answer 12

@Ferredoxin4 how you think than may be given the length of radius equal 1 cm may be possibile writing the length of this line more easy or just so with out any length of radius using r may be possibile writing a relation between circumference and the length of this line or something in this way ???? thank you in advance all your help

Answer 13

I'm back.


Just found out that this question has been answered before. It has the similar explanation to mine. View this:
https://math.stackexchange.com/questions/1885357/tennis-ball-shape-math-problem

Forget what I said about drawing a net, that's wayy too complicated. Instead there's a much better approach. If you think about it, the white seam could be a parametric function. We could find the line length, but I'm not equipped with skills to figure that out as I haven't taken multivariable calculus. Still, this method is solved too:

https://math.stackexchange.com/questions/316531/parametric-curve-for-a-tennis-ball-seam/316612

Answer 14

Interesting question though, I've never thought of it myself.

Answer 15

@Ferredoxin4 thank you very much

Answer 16

@Ferredoxin4 here is my idea :

looke please on image 1 and 4 ,than we unit togheter this two semicircle formed by this lines we get a circle and so in this way than you see the image 2 with 3 so we get and second circle formed by this lines

suppose the cicumference of this ball is 2piR where R is the radius of the ball

and let r being the radius of this circle formed by this lines so how you think what may be
the relation between R and r ?

may be possibile R = 2r or R = 3r or ..???

and so in this way than we can getting the radius of this circles formed by this line ( these semicircles ) so may be more easy getting the length of this line (my idea )

your opinion please ???? thank you in advance

Answer 17

I'll get back to you on your comment.

You might want to see this:
https://www.youtube.com/watch?v=A5sCQ_ZCh0U
http://mathforum.org/kb/message.jspa?messageID=554042

And calculate the arc length. It's going to be a long process though. I'm not sure if there's any other way and I can't think of any either.

Answer 18

@imqwerty any idea in this problem ? and so opinions about above wrote ???

Answer 19

@Tranquility any idea in this case please ?