Nursery Rhymes And Venn Diagrams

It started, as these things are wont to do, with a completely innocent conversation. It started with sonnets and somehow moved onto other poetry.
“All nursery rhymes are poems but not all poems are nursery rhymes” was the sentence that caught my attention as my imagination invariably started drawing a Venn diagram.  Next, my mind added “Sonnets” into the picture which left the obvious question. Was there anything in the intersection? Is NurseryRhymes \cap Sonnets = \emptyset ?

Poetry Venn Diagram

There are several ways to answer this question but my solution is to attempt to fill the intersection by writing the following:

Sonnet IV – Humpty’s Fall

When Humpty Dumpty seated was on high
Upon a wall of bricks so wide and tall,
So unexpected did things go awry
And Humpty thus did fall from off the wall.
Fair rapidly he tumbled to the ground
Impacting with a most almighty crash,
With tiny pieces scattered all around
The ground was littered when his shell did smash.
Now to his aid did men and horses run
Sent by the king to help this needy soul.
Alas, assistance could they give him none,
They couldst not succour him nor make him whole.
So endeth Humpty Dumpty’s tragic tale
Which have I here the honour to regale.

© CMB

Possibly a little silly but it was fun to try and make it work. What do you think?

Advertisements

How I Wish I Could Calculate Pi

So as part of Pi day (and I will restrain my frustration at the American style date format that is needed to make this appropriate) Oxford university decided it would be a good idea to have a huge experiment to calculate pi. They suggested four ways that this could be achieved the idea being that you have a go at one of them and then all the results would be collated to see what the average was. I decided to have a go at several of them.

Circles

Take a circular object and some string and measure the circumference and diameter. This is the most direct method and ought to be fairly accurate. I decided to use a Denby dinner plate and measured it with a handy piece of string.

Result: Circumference = 84.5cm, diameter = 26.5 cm, pi = 3.188

MarblesMarbles

Use marbles to fill a circle and therefore measure the area. I used the aforementioned plate (cunning eh) and filled it with marbles. I tried to use marbles of approximately the same size but had to rely on eye (and hand) to judge the size.

Result: Total marbles 132, diameter 13 marbles, pi = 3.124

Needles

Drop a needle like thing onto a piece of paper – a lot and see if it crosses some lines. I dropped the needle 100 times and got the below result. I then tried a further 100 and got exactly the same outcome. I decided to quit while I was ahead.

Result: Distance between lines = 50mm, length of needle = 26 mm, dropped 100 times crossed lines 26 times, pi = 3.586

Rivers

This asked us to measure the ratio of a river’s full length to ‘as the crow flies’ distance covered. This isn’t so much calculating pi as seeing whether the length of the river really has some relationship to it. While it is possible that over a long distance a river may tend to this ratio it is easy to see if you divide a river into two that the equation may not work equally well for each half (imagine that the river bends at around the dividing point and the geometry is obvious). Given that I’m not convinced that this would give a very satisfactory answer – and anyway I ran out of time.

Mind you I already know what pi should be, can you tell?