Garden-variety mathematics

A mathematics teacher of mine once told with some pride about the first and last time he had used mathematics for a practical purpose. It concerned calculating the length of the rope he needed to tie his houseboat to the quay. For this he had used Pythagoras' theorem. His use of Pythagoras' theorem makes it part of  what I call garden-variety mathematics: mathematics used for a practical purpose, at home for example. Let me expand garden-variety mathematics with two more examples.

A woman recently told me that she needed a ladder for rebuilding her house. She had to know the length of this ladder and calculated it with the 'sine' function. This was the first time this goniometric function was of practical use for her, outside the class room. Moreover, she discovered that she got the same answer with the 'cosine'!
Hence, garden-variety mathematics minimally consists of Pythagoras' theorem and a part of trigonometry: the sine and cosine functions.

Now of course I cannot stay behind. So here you have it, the bookcase  I developed myself:

At first sight the division of shelves may seem a bit strange, therefore, let me explain the rationale behind it. First of all, I liked to store as many books in it as the total space could accommodate. As a consequence, there should for example not be many high compartments with only small pocket books in them. To solve this optimization problem I made a histogram of the height of my books. Discerning three sizes - small, medium, large - gave the following proportions:

small:medium:large= 11:8:2

The proportions do not fix the compartment division exactly. The precise shape followed from demanding that it is robust and foremost: that it should please the eye. With respect to the latter, it pleases my eye because of the four overlapping stair cases each consisting of three ascending horizontal steps. What also adds to the beauty is the near mirror symmetry around horizontal and vertical lines through the centre. Less obvious is the exact 180 degree rotational symmetry around the centre. 

Ok, with this contribution I expanded garden-variety mathematics to Pythagoras' theorem, some trigonometry, histograms  and a bit of geometry. Who can add to this?


This article is a translation of  http://nietexact.blogspot.nl/2014/08/huis-tuin-en-keuken-wiskunde.html (August 17, 2014).