# Tag Info

### Good, simple examples of induction?

Simple proofs (Proofs 1-3) Bernoulli Inequality Inequality of AM - GM (There various proof using mathematical induction. You can use standard induction or forward-backward induction.) Newton's ...
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### Good, simple examples of induction?

1)Finitely many lines divide a plane into regions. Show these regions can be coloured by two colours in such a way that neighboring regions have different colours. 2)Showthat there are $2^n%$ number ...

### Surprising examples of Cavalieri's principle

This example here I discovered myself: Consider a cylinder of radius $r$ and height $h$, circumscribing a paraboloid $y=h\left(\dfrac{x}{r}\right)^2$ whose apex is at the center of the bottom base of ...
1 vote

### Applications of Triangle Inequality for high-school students?

Here are two examples (one for your one-dimensional question and one in 2D, which is not really what you are asking about) Consider the following (not really lifelike) situation. There are two shops ...
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At its most basic, the Triangle Inequality says that it is (in general) a shorter trip to go directly from point $A$ to point $B$ than it would be to stop at point $C$ in between. That is, the length ...