1

Can somebody tell me how to measure the length of a thread which is wrapped around 4 circles the radius of each is 1m. The four circles are touching but their centers don't form a square when they are connected. Can you please explain the steps and the laws you use when you measure the length of that thread an thanks.

adib
  • 23
  • So what DO the centers form? What do we know about these circles? – Kaynex Mar 16 '16 at 02:59
  • 1
    As long as the 4 circles are arranged like a ring (circle 1 touching 2, circle 2 touching 3, circle 3 touching 4 and circle 4 touching 1 again). Your thread will be composed of 4 line segments and 4 circular arcs. Convince yourself the length of each line segment is equal to the distance between the centers of two circles and the 4 circular arcs can be translated/rotated to combine into a single circle. – achille hui Mar 16 '16 at 03:06

1 Answers1

0

Here is a figure to help with achille hui's comment, which is what I was goin write. Note that DE and IH are the distance between the centers.

enter image description here

Ross Millikan
  • 374,822
  • Isn't there a way to know the arc's measure just by the number of circles? – adib Mar 17 '16 at 15:33
  • Not if you don't assume the centers form a specific polygon. For four circles you could have a square, where each arc is a.quarter circle, but you could also have a parallelogram with different angles. – Ross Millikan Mar 17 '16 at 16:04
  • Thanks for your clarification :) – adib Mar 17 '16 at 16:16