# Resources tagged with: Iteration

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##### Other tags that relate to LOGO Challenge - Sequences and Pentagrams
Mathematical reasoning & proof. Visualising. Logo. Programming. Working systematically. Combinatorics. STEM - General. Networks/Graph Theory. Practical Activity. Iteration.

### There are 13 results

Broad Topics > Patterns, Sequences and Structure > Iteration ### Difference Dynamics

##### Age 14 to 18 Challenge Level:

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? ### First Forward Into Logo 1: Square Five

##### Age 7 to 16 Challenge Level:

A Short introduction to using Logo. This is the first in a twelve part series. ### First Forward Into Logo 10: Count up - Count Down

##### Age 11 to 18 Challenge Level:

What happens when a procedure calls itself? ### Differs

##### Age 11 to 14 Challenge Level:

Choose any 4 whole numbers and take the difference between consecutive numbers, ending with the difference between the first and the last numbers. What happens when you repeat this process over and. . . . ### Stringing it Out

##### Age 14 to 16 Challenge Level:

Explore the transformations and comment on what you find. ### Loopy

##### Age 14 to 16 Challenge Level:

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? ### Dalmatians

##### Age 14 to 18 Challenge Level:

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. ### The Golden Ratio, Fibonacci Numbers and Continued Fractions.

##### Age 14 to 16

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions. ### Slippage

##### Age 14 to 16 Challenge Level:

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . . ### Converging Means

##### Age 14 to 16 Challenge Level:

Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . . ### Triangle Incircle Iteration

##### Age 14 to 16 Challenge Level:

Keep constructing triangles in the incircle of the previous triangle. What happens? ### Peaches in General

##### Age 14 to 16 Challenge Level:

It's like 'Peaches Today, Peaches Tomorrow' but interestingly generalized. ### Stretching Fractions

##### Age 14 to 16 Challenge Level:

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?