# Tagged Questions

For questions concerning the creation and understanding of pictorial proofs.

2answers
72 views

### Proof without words for logarithmic funtions [closed]

I'm looking for a PROOF WITHOUT words for logarithms. The only one I've seen is calculus based and I need one for a younger audience. Any help/suggestions would be appreciated! This is the example I ...
4answers
96 views

### To prove $\frac{n!}{p!q!}$. [closed]

The number of permutaion of n objects, where p and are of one kind,q are of second kind,are of different kind is $\frac{n!}{p!q!}$ How can we proove above theorem $\frac{n!}{p!q!}$.I tried to prove ...
4answers
185 views

### Geometric proof of $QM \ge AM$

Prove by geometric reasoning that: $$\sqrt{\frac{a^2 + b^2}{2}} \ge \frac{a + b}{2}$$ The proof should be different than one well known from Wikipedia: DISCLAIMER: I think I devised such proof (...
0answers
114 views

### Using a visual “proof” to show that $\sum_{n=1}^{\infty} \left(\frac 34 \right)^n =1$

The "proof without words" that $\sum_{n=1}^{\infty} \left(\frac 12 \right)^n =1$ is fairly well known: But why can't we apply the exact same logic to $\sum_{n=1}^{\infty} \left(\frac 34 \right)^n$ ...
2answers
1k views

### Visual proof of $\sum_{n=1}^\infty \frac{1}{n^4} = \frac{\pi^4}{90}$?

In his gorgeous paper "How to compute $\sum \frac{1}{n^2}$ by solving triangles", Mikael Passare offers this idea for proving $\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$: Proof of equality ...
1answer
87 views

### On equilateral triangles

I came across the following geometry problem. In the exterior of a triangle $ABC$ three equilateral triangles $ABC' , BCA'$ and $CAB'$ are constructed. Prove that the centroids of these triangles ...
2answers
202 views

### Explain this calculus proof without words

This demonstrates that $\int_0^1 t^{p/q} + t^{q/p} dt = 1$. Could you please explain how the proof without words shows that?
1answer
49 views

### I can't figure how to prove this coordinate algebraic geometry proof.

Consider the points $A$ and $C$ are on $y=x^p$. We are told that point $A$ has coordinates $( a, b )$, where $0<a<1$ and point $C$ has coordinates $( c, d )$, where $1<c$. Give a ...
0answers
219 views

### Looking for proof-without-words of Bezout's identity

I'm looking for a "proof-without-words" of Bezout's identity (for integers). Does anyone know of one?
1answer
98 views

4answers
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### Proof-without-words for $\bar a\times (\bar b\times\bar c)=\bar b (\bar a\cdot\bar c)-\bar c (\bar a\cdot \bar b)$ or some visual-biased explanation?

Griffiths' Introduction to Electromagnetism -book has equations called 20.10 below. I have proved this equation d) pretty much on the first mathematics -course I had but I have not yet understood a ...