# History and Culture

## Resources based on the rich history of mathematics and its place in different cultures

Characters & Concepts | Codes & Ciphers | National Lottery | Mathemagic | Pascal's Triangle | Fibonacci Numbers | National Lottery | Mathematician of the Month | Maths Trail

## Mathematical Characters and Concepts

- Mandelbrot's Mathematics
- Thales' Theorem
- al Khwarizmi's Algebra
- Goldbach's Conjectures
- Leonardo de Pisa
- Pascal and the Triangle
- The Koch Snowflake

## Codes and Ciphers - Frequency Analysis

- First, a series of posters on the History of Codes. You will need these two graphs to make any sense of them.
- This ultimate aim of the code-breaking series is aimed at Year 9. The 'Babington Plot' is a great story from history that is begging to be used in the maths classroom. Here are the teacher notes.
- This is (supposedly) a copy of the real note written by Mary Queen of Scots to Anthony Babington
- A Caesar Wheel to cut out and use. You also need this worksheet.
- The starter for lesson 2 is here
- A story from another era of code-breaking, to be used with this worksheet and this spreadsheet
- The encrypted messages worksheet uses puzzles from Simon Singh's website. You need this spreadsheet to complete the activity.
- This final worksheet includes all the symbols that occur on the Babington note
- Codes and Ciphers overview

## Codes and Ciphers - Everyday Codes

- The Maths behind barcodes and ISBN's is revealed through this series aimed at Year 8. The teacher notes are essential reading!
- A slideshow that demonstrates the barcode algorithm at work.
- The worksheet for lesson 1 is here.
- And the worksheet for lesson 2 is here.
- A spreadsheet that will find the last digit of an ISBN. Program your own in lesson 3!
- And finally, this spreadsheet tests the validity of an ISBN. Not quite as exciting to create, but good to use as a demonstration when introducing ISBN's.
- Codes and Ciphers overview

## Codes and Ciphers - Scrambling and Hiding

- The first in a series of themed lessons (this is aimed at Year 7). Look through the teacher notes here.
- This PowerPoint is needed for the first lesson. Visit the University of Exeter's website for further activites as suggested in the overview.
- Codes and Ciphers overview

## The National Lottery

- Extensive teacher notes for a possible project. This is designed to cover many of those awkward data handling objectives!
- A game - 'The Nice Lottery' - which is good to start a series of themed lessons
- A list of the results from every draw between November 1995 and June 2004. You will need this if you are following the teacher notes.

## Mathemagic

- Teacher notes for a possible project. They refer to the following files:
- A selection of magical mind-reading tasks to amaze your classes. You only need to be good at basic arithmetic - no mind-reading needed! If you want to explain your powers (using the magic of algebra), this PowerPoint will help.
- More mind-reading. The carrot and elephant tricks described in the teacher notes are here.
- If you haven't yet exhausted your imaginary telepathic capabilities, you might want these (binary) mind-reading cards too.
- Okay, on to the vanishing tricks. This great activity gives one shape with an area of either 58, 59 or 60 squares, depending on how you arrange it. It is known as the Curry Triangle.
- Another area conundrum - Fibonacci's disappearing squares.
- If those don't amaze and enthrall (and they certainly should!) this vanishing leprechaun trick is superb. Put it onto an acetate for best results
- This missing person trick is very similar to the leprechauns. It is in three parts; 1, 2, 3
- If you feel up to it, try making cards disappear too with this clever trick
- A magic theme wouldn't be complete without some magic squares. Here is a slideshow to introduce the concept of a magic square.
- Here is the magic square challenge from the National Numeracy Stategy.
- And finally, guaranteed to fool even the brightest pupils (well probably), take a look at this addition trick.

## Pascal's Triangle

- A mostly blank template to be filled in.
- The first 12 rows, with rows and diagonals numbered.
- The first 50 rows displayed on a spreadsheet. All the odd numbers are shaded a different colour producing a lovely fractal. You can vary the conditional formatting to shade multiples of other numbers and get different patterns.
- The first 50 rows modelled differently on a spreadsheet. Rows and diagonals labelled - the magic lottery figure highlighted.
- One investigation that yields the triangle - counting the number of different ways of jumping up staircases.
- Some of the magical properties that exist in the triangle are noted here.
- Mathematician of the Month: Pascal
- Characters and Concepts: Pascal and the Triangle

## Fibonacci Numbers and the Golden Ratio

- Fibonacci numbers and the male bee
- Constructing a golden rectangle and a golden spiral
- Find the golden ratio in yourself
- Investigate the golden star
- An picture to demonstrate Fibonacci numbers in the spirals of a pine cone.
- Mathematician of the Month: Fibonacci
- Characters and Concepts: Leonardo de Pisa

## Mathematician of the Month

- Mr January: Fermat - and his big problem
- Mr February: Galois - young and foolish?
- Mr March: Fibonacci - rabbits, rabbits, rabbits
- Mr April: Pascal - nearly invented the sandwich
- Mr May: Descartes - a fan of beef tea
- Mr June: Pythagoras - you need this too
- Mr July: Babbage - monster calculator
- Mr September: Newton - England's finest
- Mr October: Archimedes - Greek genius
- Mr November: Ramanujan - and the number 1729
- Miss December: Somerville - and the arctic island

### Some alternatives!

- Mr January: Gauss - child prodigy
- Mr May: Jones - unsurprisingly Welsh
- Mr October: Mandelbrot - A fractal name?
- Mr November: Polya - Professor Euclide Paracelso Bobasto Umbugio of Guayazuela?
- Mr December: Heron - prolific inventor

The following publications were invaluable sources of information in the production of 'Mathematician of the Month'; Historical Connections in Mathematics, volumes 1, 2 & 3, by Wilbert Reimer and Luetta Reimer; Men of Mathematics, volumes 1 & 2, by E.T.Bell.

## Maths Trail

- This Maths Trail was written for Lincoln city centre, but the ideas can easily be adapted for other towns and cities.