# Resources tagged with: Proof by contradiction

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### There are 10 results ### Eyes Down

##### 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? ### Tetra Inequalities

##### 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. ### Staircase

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

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

##### 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. ### Impossible Square?

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

Can you make a square from these triangles? ### Proof Sorter - the Square Root of 2 Is Irrational

##### 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. ### An Introduction to Proof by Contradiction

##### Age 14 to 18

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

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

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

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

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

##### 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.