Recent questions in Chords

Chords
Answered

Rosemary Chase
2022-11-15

From a specific point A on a circle's circumference, am drawing various chords. a) what is the sum of length of such chords and b) what is the average length of such chords?

Assuming a radius r, I'm trying to solve a) in the below manner:

One specific chord length $=2r\mathrm{cos}(\mathrm{\Theta})$

To get the sum, I'm integrating over $-\pi /2\text{}to\text{}\pi /2(2r\mathrm{cos}(\mathrm{\Theta})d\mathrm{\Theta})$

But i don't think this is right. Please point me in the correct direction.

Chords
Answered

Maribel Vang
2022-10-29

Some thoughts:

Its not clear to me as to why f(n) is well defined.

$f(n)=f(n-1)+$ something. I want to determine that something.

Is f(n) an upper bound for the crossing number of ${K}_{n}$?

Chords
Answered

Mattie Monroe
2022-10-27

Suppose that I have a very special Ukulele that contains N frets. I can use atmost 4 fingers to play a chord. I am required to determine the total number of different chords that I can play.

Note: Two chords are different if one of the frets that are pressed in one of the chords is not pressed in another chord.