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Sunday, 23 March 2014

Sunday Afternoon Maths V

Here's this week's collection. Answers & extensions here. Why not discuss the problems on Twitter using #SundayAfternoonMaths.

Two Lines

Let A and B be two straight lines such that the gradient of A is the y-intercept of B and the y-intercept of A is the gradient of B (the gradient and y-intercept of A are not the same). What are the co-ordinates of the point where the lines meet?

Odd Sums

What is (1+3) ÷ (5+7)?
What is (1+3+5) ÷ (7+9+11)?
What is (1+3+5+7) ÷ (9+11+13+15)?
What is (1+3+5+7+9) ÷ (11+13+15+17+19)?
What is (sum of the first n odd numbers) ÷ (sum of the next n odd numbers)?

xxxxxx... Again

Let y = xxxxxx... [x to the power of (x to the power of (x to the power of (x to the power of (...)))) with an infinite number of xs]. What is dy/dx?

Folding Tube Maps

Back in 2012, I posted instructions for folding a tetrahedron from tube maps. When tube maps are used, the sides of the tetrahedron are not quite equal. What ratio would the rectangular maps need to be in to give a regular tetrahedron?

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