# Search by Topic

#### Resources tagged with Proof by contradiction similar to Eyes Down:

Filter by: Content type:
Stage:
Challenge level:

### Eyes Down

##### Stage: 5 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?

### Tetra Inequalities

##### Stage: 5 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.

### Rarity

##### Stage: 5 Challenge Level:

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

### Rational Round

##### Stage: 5 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.

### An Introduction to Proof by Contradiction

##### Stage: 4 and 5

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

### Staircase

##### Stage: 5 Challenge Level:

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

### Proximity

##### Stage: 4 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.

### Be Reasonable

##### Stage: 5 Challenge Level:

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

### Proof Sorter - the Square Root of 2 Is Irrational

##### Stage: 5 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.

### Impossible Square?

##### Stage: 5 Challenge Level:

Can you make a square from these triangles?