Choosing Vertices of a Polygon from Random Points on a Circle: How Many Ways?

  • Thread starter Thread starter physicsss
  • Start date Start date
AI Thread Summary
To determine the number of ways to form polygons from random points on a circle, the discussion emphasizes using 'n' to represent the total number of points. For any r-sided polygon, the formula involves combinations, specifically choosing r points from n. The conversation highlights the need for a correct formula to calculate specific answers based on varying values of n. Understanding this combinatorial approach is essential for solving the problem accurately. The focus remains on deriving a general formula applicable to different polygon types.
physicsss
Messages
319
Reaction score
0
"Number of ways" question

A circle has random points on its circumferance. How many ways can you form a quadrilateral, a triangle, and a octagon using these points?

I have no idea how to get an numerical answers for this question without using n to represent the number of points on the circle.

Thanks.
 
Physics news on Phys.org
I think using 'n' is fine...just make a correct formula such that for any n you can get a specific answer.
 
Of course you need n.
In how many ways can you choose the vertices of an r sided polygon from n points ?
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Choose a ball at random from a randomly selected box - alternative way
Replies
10
Views
2K
B: Calculate the distance between two points without using a coordinate system
Replies
20
Views
3K
How Do Three Tangents Form an Equilateral Triangle Around a Circle?
Replies
7
Views
3K
Perimeter relationships -- Dividing a rectangle into 4 triangles
Replies
2
Views
2K
No. of quadrilaterals in a polygon
Replies
1
Views
3K
In how many ways can 5 prizes be given away to 4 boys?
Replies
16
Views
2K
A Area distribution of inscribed triangles in a circumference
Replies
12
Views
2K
Calculating the distance from a point to a plane
Replies
1
Views
2K
I Given three random numbers between 0 and 1, how to evenly populate a sphere?
Replies
15
Views
2K
Algebraic expression for triangles within polygons
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top