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Proof of Leibniz $\pi$ formula
I found the following proof online for Leibniz's formula for $\pi$: $$\frac{1}{1-y}=1+y+y^2+y^3+\ldots$$ Substitute $y=-x^2$: $$\frac{1}{1+x^2}=1-x^2...
Apr 16, 2026
Archive: News
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Half distance between two points in space
Given two points $A=(x_1, y_1, z_1)$ and $B=(x_2, y_2, z_2)$ on the tridimensional space how can I get the coordinates of the point located exactly on the...
Apr 16, 2026
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Finding the false statement
There are 5 statements: A. Statement B, C, or D is false. B. If statement C is false, then statement D is true. C. It is not true that statement E is fals...
Apr 16, 2026
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Why does parenthesis before exponents not apply to squaring a binomial?
This must be a stupid question with an obvious answer that is hidden from me. No one I have found even mentions a conflict. lets say I want to find the sq...
Apr 16, 2026
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limit of the sequence $a_n=1+\frac{1}{a_{n-1}}$ and $a_1=1$
Problem: Find with proof limit of the sequence $a_n=1+\frac{1}{a_{n-1}}$ with $a_1=1$ or show that the limit does not exist. My attempt: I have failed to ...
Apr 16, 2026
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Real-life, every day applications of number theory?
Are there any day to day situations in which number theory could be applied to? For example, I was trying to make a mosaic and I realized that diophantine...
Apr 16, 2026
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How to calculate the radius of a circle inscribed in a regular hexagon?
If I know how long one side of a regular hexagon is, what's the formula to calculate the radius of a circle inscribed inside it? Illustration:
Apr 16, 2026
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How is a nonnegative orthant a cone?
My textbook says the following: The nonnegative orthant is the set of points with nonnegative components, i.e., $$\mathbb{R}_+^n = \{ x \in \mathbb{R}^n \...
Apr 16, 2026
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Combinations of lottery balls?
I'm studying for a final and practicing on old exam. I am having trouble with a question. "There is a lottery game that consists of two sets of numbe...
Apr 16, 2026
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a question about the surface area of two Octagonal pyramids
A friend of mine came to me with a problem earlier today and I'm unsure if the answer I arrived at was correct. I simply found a formula on wolfram a...
Apr 16, 2026
