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Resources tagged with Proof by contradiction similar to Eyes Down:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Using, Applying and Reasoning about Mathematics > Proof by contradiction

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Eyes Down

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Rarity

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Rational Round

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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An Introduction to Proof by Contradiction

Stage: 4 and 5

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

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Staircase

Stage: 5 Challenge Level: Challenge Level:1

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

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Proximity

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Tetra Inequalities

Stage: 5 Challenge Level: Challenge Level:1

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.

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Be Reasonable

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Proof Sorter - the Square Root of 2 Is Irrational

Stage: 5 Challenge Level: Challenge Level:1

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.

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Impossible Square?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make a square from these triangles?