mscroggs.co.uk
mscroggs.co.uk

subscribe

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?

Show answer & extension

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 \(\frac{dy}{dx}\)?

Show answer & extension

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 \(\frac{\mathrm{sum\ of\ the\ first\ }n\mathrm{\ odd\ numbers}}{\mathrm{sum\ of\ the\ next\ }n\mathrm{\ odd\ numbers}}\)?

Show answer & extension

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?

Show answer & extension

If you enjoyed these puzzles, check out Advent calendar 2023,
puzzles about dominos, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

integration division quadratics percentages logic polygons range cubics circles rugby area addition chalkdust crossnumber cryptic clues polynomials graphs triangles partitions cards bases pascal's triangle wordplay floors trigonometry dates probability indices 3d shapes people maths decahedra tiling coins sets digital clocks median expansions routes factors pentagons triangle numbers matrices differentiation time money tournaments geometry star numbers angles albgebra dominos dice speed calculus irreducible numbers consecutive integers perimeter hexagons advent factorials sequences even numbers the only crossnumber gerrymandering 2d shapes colouring sums rectangles determinants surds cryptic crossnumbers square numbers complex numbers scales combinatorics geometric means square roots fractions elections cube numbers chocolate numbers doubling chess palindromes probabilty digital products volume dodecagons algebra functions shape products quadrilaterals lines proportion multiples planes grids axes christmas ave remainders consecutive numbers regular shapes crosswords parabolas integers sum to infinity sport coordinates balancing number digits folding tube maps means books spheres symmetry unit fractions ellipses squares crossnumber odd numbers games menace perfect numbers multiplication prime numbers taxicab geometry crossnumbers binary averages shapes geometric mean mean clocks tangents arrows

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024