- Irrationality Of E 17/10/2010 01:00
Prove that e is irrational.

Problem ID: 377 (17 Oct 2010) / Difficulty: 4 star - Rectangle Construction 17/10/2010 01:00
Find the connection between the constructed length and the original rectangle.

Problem ID: 376 (17 Oct 2010) / Difficulty: 2 star - Inscribed Circle In Isosceles Triangle 16/08/2010 01:00
Find the radius of the circle inscribed inside the isosceles triangle.

Problem ID: 375 (16 Aug 2010) / Difficulty: 2 star - Multiplying Magic Square 16/08/2010 01:00
Show how the values 1, 2, 4, 8, 16, 32, 64, 128, and 256 can be placed in a 3x3 square grid so that the product of each row, column, and diagonal gives the same value.

Problem ID: 374 (16 Aug 2010) / Difficulty: 3 star - Polynomial Roots 07/08/2010 01:00
Prove that the roots of the polynomial, x

Problem ID: 373 (07 Aug 2010) / Difficulty: 3 star^{n}+ c_{n-1}x^{n-1}+ ... + c_{2}x^{2}+ c_{1}x + c_{0}= 0, are irrational or integer. - Hops And Slides But Never Square 07/08/2010 01:00
Prove that the minimum number of moves to completely reverse the positions of the coloured counters can never be square.

Problem ID: 372 (07 Aug 2010) / Difficulty: 3 star - Irrationality Of Pi 24/12/2009
Prove that π is irrational.

Problem ID: 371 (24 Dec 2009) / Difficulty: 4 star - Square And Round Plugs 24/12/2009
Which fits better... a round plug in a square hole or a square plug in a round hole?

Problem ID: 370 (24 Dec 2009) / Difficulty: 2 star - Algebraic Cosine 30/11/2009
Prove that cos(x) is algebraic if x is a rational multiple of Pi.

Problem ID: 369 (30 Nov 2009) / Difficulty: 4 star - Inscribed Square 30/11/2009
Find the side length of the square inscribed inside the right angled triangle.

Problem ID: 368 (30 Nov 2009) / Difficulty: 2 star - Infinite Circles 15/11/2009
What fraction of the large red circle do the infinite set of smaller circles represent?

Problem ID: 367 (15 Nov 2009) / Difficulty: 4 star

- Finding Circles 01/03/2015 00:00Can you find the centre and equation of a circle given a number of points on the circle? When is it possible and when is it not?
- The Circle of Apollonius... Coordinate Edition 01/03/2015 00:00Can you sketch and then find an equation for the locus of a point based on its distance from two fixed points?
- Equation or Identity (1) 01/12/1999 00:00Which of these equations concerning the angles of triangles are always true?
- Equation or Identity (2) 01/12/1999 00:00Here are some more triangle equations. Which are always true?
- Have a Sine 01/12/1999 00:00There's much more to trigonometry than sin, cos and tan...
- Factorial Fragments 01/12/2014 00:00Here you have an expression containing logs and factorials! What can you do with it?
- Approaching Asymptotes 01/11/2014 00:00Can you describe what an asymptote is? This resource includes a list of statements about asymptotes and a collection of graphs, some of which have asymptotes. Use the graphs to help you decide whether you agree with the statements about asymptotes.
- Two-way Functions 01/11/2014 00:00This gives you an opportunity to explore roots and asymptotes of functions, both by identifying properties that functions have in common and also by trying to find functions that have particular properties. You may like to use the list of functions in the Hint, which includes enough functions to complete the table plus some extras.You might like to work on this problem in a pair or small group, or to compare your table to someone else's to see where you have used the same functions and where not.
- Giants Poster 01/09/2014 00:00
- Discriminating 01/09/2014 00:00You're invited to decide whether statements about the number of solutions of a quadratic equation is always, sometimes or never true.
- Factorisable Quadratics 01/09/2014 00:00This will encourage you to think about whether all quadratics can be factorised and to develop a better understanding of the effect that changing the coefficients has on the factorised form.
- Which Quadratic? 01/09/2014 00:00In this activity you will need to work in a group to connect different representations of quadratics.
- Absolutely! 01/11/2014 00:00What can you say about this graph? A number of questions have been suggested to help you look at the graph in different ways. Use these to help you make sense of this and similar graphs.
- Picture the Process I 01/11/2014 00:00How does the temperature of a cup of tea behave over time? What is the radius of a spherical balloon as it is inflated? What is the distance fallen by a parachutist after jumping out of a plane? After sketching graphs for these and other real-world processes, you are offered a selection of equations to match to these graphs and processes.
- Nine Eigen 01/02/2011 00:00Explore how matrices can fix vectors and vector directions.

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- Boots or Heels: My Wardrobe Paradox as a Woman in STEM 14/04/2015 14:17
- Was I Wrong about “The End of Science”? 13/04/2015 15:29
- ScienceDebate Revs Up for 2016 Presidential Election 13/04/2015 14:32
- Mathematicians Chase Moonshine’s Shadow 07/04/2015 14:30
- Against April Fools' in Science Journalism 01/04/2015 15:10
- The Cantor Function: Angel or Devil? 31/03/2015 13:00
- A Few of My Favorite Spaces: The Cantor Set 26/03/2015 12:30
- The Science of TED 2015 23/03/2015 14:00
- What’s so Great about Continued Fractions? 17/03/2015 12:30
- The Best Pi Day Pies and Celebrations 16/03/2015 20:45
- Irrational Exuberance: How Will You Celebrate the Pi Day of the Century? 14/03/2015 13:26
- The Pi Day of the Century 13/03/2015 13:15
- American Pi: Why the Day Belongs to the U.S. (and Belize) 12/03/2015 13:54
- Don’t Recite Digits to Celebrate Pi. Recite Its Continued Fraction Instead. 11/03/2015 12:30
- A Glimpse into How Mathematicians Party [Excerpt] 06/03/2015 15:00
- Uber, but for Topological Spaces 01/03/2015 01:00
- Things to Make and Do in the Fourth Dimension (Book Review) 26/02/2015 23:00
- Game Theory Calls Cooperation into Question 23/02/2015 19:00
- It's Time for More Racial Diversity in STEM Toys 23/02/2015 18:00
- 15 Surprises about Scientific American 22/02/2015 17:52
- Physics Week in Review (Valentine’s Edition): February 14, 2015 14/02/2015 10:43
- Is AI Dangerous? That Depends… 13/02/2015 16:38
- Gauss and Germain on Pleasure and Passion 13/02/2015 13:30
- How to Choose the Form of an Infographic: It's All about Context 10/02/2015 14:00