Send the link below via email or IMCopy
Present to your audienceStart remote presentation
- Invited audience members will follow you as you navigate and present
- People invited to a presentation do not need a Prezi account
- This link expires 10 minutes after you close the presentation
- A maximum of 30 users can follow your presentation
- Learn more about this feature in our knowledge base article
Transcript of What are...?
. Defining features:
- Formed of n circles of the same size all overlapping a common point equally where
is always a whole number
- Each individual group has a distinct number of pieces, small sections formed by the overlapping of the circles’ lines.
- As more circles are added, the number of pieces increases and individual pieces become smaller.
We faced few but difficult obstacles
- What we started with was not what we ended with
- Only one of us could reproduce the figures
- The larger the circle got the harder it was to count the pieces
Though we experienced trouble we had many breakthroughs
Andrew Mitchell & Kenneth Tynan
2 circles- 3 pieces
3 circles- 7 pieces
4 circles- 13 pieces
5 circles- 21 pieces
6 pieces- 31 pieces
7 pieces- 43 pieces
8 pieces- 57 pieces
9 pieces- 73 pieces
10 pieces- 91 pieces
(n) Circles = (P) Pieces
1 circles - 1 increase
2 circles - 2 increase
3 circles - 4 increase
4 circles - 6 increase
5 circles - 8 increase
6 circles - 10 increase
7 circles - 12 increase
8 circles - 14 increase
9 circles - 16 increase
10 circles - 18 increase
There is an increase of 2 pieces when a new circle is added
Equation of P for value of n
91 = 10 × 9 + 1
- Eclipse groups have 2n symmetrical actions; rotation and reflection
- The Eclipse groups will develop a n-sided polygon in the center with that has curved sides.
(proved up to n=10)
Areas of Further Study
- Will our proofs hold true the conjectures for all values of n?
- Will n continuously increase by multiples of 2?
- How is the pattern in the increasing number of pieces related to the equation we found?
- How do the pieces change size with the addition of more circles? Is there a pattern or ratio?
- Can we produce similar results with different overlapping patterns?