BMAD

All you showed is the bound is wider than one thought.

So then if we know N and P we should be able to bound squares x by a two values. Are those values always consecutive?

I agree

Find a function where the arc lenth and area between any two randomly defined points is the same. There are two.

Say we have the function: y=x^x^x^x^x..... Find an x value for which the derivative of this function converges. If you are really clever you'll find the interval that converges.

Hmmmm, my answer was the reciprocal of yours. Maybe I am wrong. Can you support your answer?

What is (-1/2)! x (-1/2)!

Write the complex form (a + bi) for: Sqrt ( i )

Find the Limit as n goes to infinity for: (1^n + 2^n + 3^n + 4^n....+ n^n) ---------------------over--------------------- (n^1+ n^2 + n^3 + n^4 ... + n^n)

I agree that it will vary but we can bound the area.

Suppose you have a triangle that has 2-1 inch lengths. Divide this triangle into half by drawing a line from vertex between the two identical sides, choose one of the sides randomly and shade it. The non-shaded side is cut in half again. Choose one of these sides randomly and cut it in half again shading one random piece. If this pattern of cut, shade, cut, cut, shade, cut, cut, shade cut, cut,.... was to be continued forever, what would be the area of the shaded region?

Maybe one of you answered this question: :) I should have included this pic though...

Suppose i have a circle. I cut off its arcs such that it became the biggest possible square i could make from that circle. What's the ratio of the edge of the circle to the middle of the edge of the square (assume minimum length) to the radius of the circle.

yes.

No they just need to be distinguishable.