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# Sunday Afternoon Maths V

Posted on 2014-03-23

## 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?

## x to the power of x again

Let $$y=x^{x^{x^{x^{...}}}}$$ [$$x$$ to the power of ($$x$$ to the power of ($$x$$ to the power of ($$x$$ to the power of ...))) with an infinite number of $$x$$s]. What is $$\frac{dy}{dx}$$?

## Odd sums

What is $$\frac{1+3}{5+7}$$?
What is $$\frac{1+3+5}{7+9+11}$$?
What is $$\frac{1+3+5+7}{9+11+13+15}$$?
What is $$\frac{1+3+5+7+9}{11+13+15+17+19}$$?
What is $$\frac{\mathrm{sum\ of\ the\ first\ }n\mathrm{\ odd\ numbers}}{\mathrm{sum\ of\ the\ next\ }n\mathrm{\ odd\ numbers}}$$?

## 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?
If you enjoyed these puzzles, check out Advent calendar 2019,
puzzles about hexagons, or a random puzzle.

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