# Resources tagged with: Proof by contradiction

### There are 10 results

Broad Topics >

Using, Applying and Reasoning about Mathematics > Proof by contradiction

##### Age 16 to 18 Challenge Level:

Prove that in every tetrahedron there is a vertex such that the
three edges meeting there have lengths which could be the sides of
a triangle.

##### Age 14 to 16 Challenge Level:

We are given a regular icosahedron having three red vertices. Show
that it has a vertex that has at least two red neighbours.

##### Age 16 to 18 Challenge Level:

Can you make a square from these triangles?

##### Age 16 to 18 Challenge Level:

The symbol [ ] means 'the integer part of'. Can the numbers [2x];
2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three
different values?

##### Age 16 to 18 Challenge Level:

Solving the equation x^3 = 3 is easy but what about solving equations with a 'staircase' of powers?

##### Age 16 to 18 Challenge Level:

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

##### Age 16 to 18 Challenge Level:

Show that it is rare for a ratio of ratios to be rational.

##### Age 16 to 18 Challenge Level:

Show that there are infinitely many rational points on the unit
circle and no rational points on the circle x^2+y^2=3.

##### Age 16 to 18 Challenge Level:

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic
progression.

##### Age 14 to 18

An introduction to proof by contradiction, a powerful method of mathematical proof.