IB Maths Resources from Intermathematics
IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides
(Header image generated from here). ECDSA: Elliptic Curve Signatures This is the second post on this topic - following on from the first post here. Read that first for more of the maths behind this! In this post I'll look at this from a computational angle - and make a simple Python code to create... Continue Reading →
https://www.youtube.com/watch?v=tkC1HHuuk7c Plotting Pi and Searching for Mona Lisa This is a very nice video from Numberphile - where they use a string of numbers (pi) to write a quick Python Turtle code to create some nice graphical representations of pi. I thought I'd quickly go through the steps required for people to do this by... Continue Reading →
Hailstone Numbers Hailstone numbers are created by the following rules: if n is even: divide by 2 if n is odd: times by 3 and add 1 We can then generate a sequence from any starting number. For example, starting with 10: 10, 5, 16, 8, 4, 2, 1, 4, 2, 1... we can see... Continue Reading →
Further investigation of the Mordell Equation This post carries on from the previous post on the Mordell Equation - so make sure you read that one first - otherwise this may not make much sense. The man pictured above (cite: Wikipedia) is Louis Mordell who studied the equations we are looking at today (and which... Continue Reading →
When do 2 squares equal 2 cubes? Following on from the hollow square investigation this time I will investigate what numbers can be written as both the sum of 2 squares, 2 cubes and 2 powers of 4. i.e a2+b2 = c3+d3 = e4+f4. Geometrically we can think of this as trying to find an... Continue Reading →
Waging war with maths: Hollow squares The picture above [US National Archives, Wikipedia] shows an example of the hollow square infantry formation which was used in wars over several hundred years. The idea was to have an outer square of men, with an inner empty square. This then allowed the men in the formation to... Continue Reading →
Computers can brute force a lot of simple mathematical problems, so I thought I'd try and write some code to solve some of them. In nearly all these cases there's probably a more elegant way of coding the problem - but these all do the job! You can run all of these with a Python... Continue Reading →
https://www.youtube.com/watch?v=q6L06pyt9CA Stacking cannonballs - solving maths with code Numberphile have recently done a video looking at the maths behind stacking cannonballs - so in this post I'll look at the code needed to solve this problem. Triangular based pyramid. A triangular based pyramid would have: 1 ball on the top layer 1 + 3 balls... Continue Reading →
https://www.youtube.com/watch?v=Wim9WJeDTHQ What's so special about 277777788888899? Numberphile have just done a nice video which combines mathematics and computer programing. The challenge is to choose any number (say 347) Then we do 3x4x7 = 84 next we do 8x4 = 32 next we do 3x2 = 6. And when we get to a single digit number... Continue Reading →
Project Euler: Coding to Solve Maths Problems Project Euler, named after one of the greatest mathematicians of all time, has been designed to bring together the twin disciplines of mathematics and coding. Computers are now become ever more integral in the field of mathematics - and now creative coding can be a method of solving... Continue Reading →