IB Maths Resources from Intermathematics
IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides
Using matrices to make fractals We start with a triangle ABC, with coordinates 𝐴(0,0) , 𝐵(1,0) , 𝐶( 0,1) as shown above. We can this triangle F_0 and we then write this as the following matrix: We then have the following algorithm to generate the next triangle F_1. In effect this means that the triangle... Continue Reading →
The Barnsley Fern: Mathematical Art This pattern of a fern pictured above was generated by a simple iterative program designed by mathematician Michael Barnsely. I downloaded the Python code from the excellent Tutorialspoint and then modified it slightly to run on repl.it. What we are seeing is the result of 40,000 individual points - each plotted... Continue Reading →
Sierpinski Triangle: A picture of infinity This pattern of a Sierpinski triangle pictured above was generated by a simple iterative program. I made it by modifying the code previously used to plot the Barnsley Fern. You can run the code I used on repl.it. What we are seeing is the result of 30,000 iterations of a simple... Continue Reading →
https://www.youtube.com/watch?v=7dcDuVyzb8Y The Coastline Paradox and Fractional Dimensions The coastline paradox arises from the difficulty of measuring shapes with complicated edges such as those of countries like the Britain. As we try and be ever more accurate in our measurement of the British coastline, we get an ever larger answer! We can see this demonstrated below:... Continue Reading →
Fractals aren't actually on the syllabus - but they do offer quite a good opportunity to look at limits, infinite sequences, complex numbers (eg Julia sets etc), the relationship between maths and art and so on. This video is a fantastic introduction to fractals - looking at how the Koch snowflake has simultaneously a finite... Continue Reading →