Other tags that relate to Proof Sorter - the Square Root of 2 Is Irrational
Coordinates. Continued fractions. Powers & roots. Proof by contradiction. Dynamic geometry. Quadratic equations. Rational and irrational numbers. Mathematical reasoning & proof. Interactivities. Complex numbers.There are 10 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Proof by contradiction
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.
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.
Be Reasonable
Age 16 to 18 Challenge Level:
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
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?
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.
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.