1 out of 3
What happens when a procedure calls itself?
1 out of 3
Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?
2 out of 3
It's like 'Peaches Today, Peaches Tomorrow' but interestingly generalized.
3 out of 3
Keep constructing triangles in the incircle of the previous triangle. What happens?
1 out of 3
Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.
1 out of 3
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
1 out of 3
How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
2 out of 3
This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.
3 out of 3
Form a sequence of vectors by multiplying each vector (using vector products) by a constant vector to get the next one in the seuence(like a GP). What happens?
3 out of 3
Can you find the link between these beautiful circle patterns and Farey Sequences?
