IB Maths Resources from Intermathematics
IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides
Finding the average distance in a polygon Over the previous couple of posts I've looked at the average distance in squares, rectangles and equilateral triangles. The logical extension to this is to consider a regular polygon with sides 1. Above is pictured a regular pentagon with sides 1 enclosed in a 2 by 2 square. ... Continue Reading →
Finding the average distance in an equilateral triangle In the previous post I looked at the average distance between 2 points in a rectangle. In this post I will investigate the average distance between 2 randomly chosen points in an equilateral triangle. Drawing a sketch. The first step is to start with an equilateral triangle... 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 →
Chaos and strange Attractors: Henon's map Henon's map was created in the 1970s to explore chaotic systems. The general form is created by the iterative formula: The classic case is when a = 1.4 and b = 0.3 i.e: To see how points are generated, let's choose a point near the origin. If we take... 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 →
Square Triangular Numbers Square triangular numbers are numbers which are both square numbers and also triangular numbers - i.e they can be arranged in a square or a triangle. The picture above (source: wikipedia) shows that 36 is both a square number and also a triangular number. The question is how many other square triangular... 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 →
Hollow Cubes investigation Hollow cubes like the picture above [reference] are an extension of the hollow squares investigation done previously. This time we can imagine a 3 dimensional stack of soldiers, and so try to work out which numbers of soldiers can be arranged into hollow cubes. Therefore what we need to find is what... 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 →