If Carlsberg made maths textbooks

If Carlsberg made maths textbooks then they would probably make something along the lines of Oliver Byrne’s edition of Euclid’s Elements. In it Byrne tries to convey the propositions and proofs of Euclid’s Elements with as few words and as many pictures as possible. To make this possible he uses colour as integral parts of his diagrams. The book’s illustrations remind me of something Peter Saville might have produced in the eighties for Factory Records or something that might have come out of the Bauhaus. The illustrations look great, yet they manage to get across some really big ideas in a clear and simplistic manner. 1664 might have been a good year for beer but 1847 was a good year for maths textbooks.

More domain and range

Here’s a link to another resource that deals with domain and range. This specifically deals with the domains and ranges of circles. The graph was created using Geogebra, which you can apparently embed into web pages. I have not worked out how to do that yet, as soon as I do I will try to embed a graph or two here.

Inverse functions

For the final lesson in the three week plan in maths we have been looking at Inverse Functions. If you missed the lesson or just didn’t get it, here is a video by a very good but very american teacher. For what is required for Core 3, you don’t need to watch any further than about 7 minutes 13 seconds.

If you find the style a bit too much and you require something a bit more sober then here are some notes.

Combined Transformations and Composite Functions

For the second week of the year twelve three week plan, here are some supporting materials on Combined Transformations and Composite Functions.

First of all a nice animation on which order to do composite functions in.

Then some extra notes on combined transformations.

Domain and Range

Following on from the year twelve lessons this week, here are some supporting materials on domain and range.

First of all, a clear and concise video explaining domain and range:

Next a link to some notes and examples on Domain and Range.

Finally a link to an activity for finding the domain and range of a function using its graph.

Freaky Maths trick

Thanks to my mate Rob for putting me onto this.

Knight Moves

Knight Moves is a mildly enjoyable thriller from the early nineties. It is also the name of one my favourite maths puzzles/investigations. The only prior knowledge required for this problem is the moves a knight can make in chess. The idea is for the knight to make it around every square on a empty board without revisiting a square. The board does not have to be a standard chess board, my favourite incarnation involves a cross shaped board.

Two of my year eleven students have produced a fantastic environment for investigating this puzzle. The environment allows you to choose the shape of your board as well as the number of players – you can either try to find the route around the board by yourself or try to trap an opponent (or opponents) into being unable to make a legal move.

The problem has been around for hundreds of years, Wikipedia seems to think it has been around since the 9th Century. A quick Google (try Knight Tour as well as Knight Moves) will reveal that quite a few people have spent quite a lot of time dedicated to this puzzle.

Little Boots

She’s over-hyped and a little bland but she has done a song called Mathematics. I do not know many songs that name check Pythagoras or Fibonacci. Honorable mention here goes to The Aphex Twin who has several tracks with mathematical names including Polynomial in C and I think Boards of Canada might have the odd track.

Hailstones

My favourite problems are the ones which are easy to describe but difficult to solve. The Hailstone Sequences problem is definitely one of these problems. It requires a basic knowledge of sequences and odd and even numbers to understand the problem yet nobody has managed to solve it.

Chocolate Maths

Here’s a neat trick sent to me by Jamie Cooke in year eight (this does make me sound like a Blue Peter presenter):
YOUR AGE BY CHOCOLATE MATH

DON’T CHEAT BY SCROLLING DOWN FIRST!
It takes less than a minute .
Work this out as you read .
Be sure you don’t read the bottom until you’ve worked it out!
This is not one of those waste of time things, it’s fun.

1. First of all, pick the number of times a week that you would like to have chocolate (more than once but less than 10)

2. Multiply this number by 2 (just to be bold)

3. Add 5

4. Multiply it by 50 — I’ll wait while you get the calculator

5. If you have already had your birthday this year add 1759 ..
If you haven’t, add 1758.

6. Now subtract the four digit year that you were born.

You should have a three digit number

The first digit of this was your original number
(i.e., how many times you want to have chocolate each week).

The next two numbers are

YOUR AGE! (Oh YES, it is!!!!!)