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#### Resources tagged with Iteration similar to Happy Numbers:

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### There are 13 results

Broad Topics > Sequences, Functions and Graphs > Iteration

### Happy Numbers

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

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

### Converging Means

##### Age 11 to 14 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. . . .

### 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?

### 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.

### Peaches in General

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

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

### 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.

### 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?

### 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.

### Triangle Incircle Iteration

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

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

### First Forward Into Logo 10: Count up - Count Down

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

What happens when a procedure calls itself?

### Weekly Challenge 48: Quorum-sensing

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

This problem explores the biology behind Rudolph's glowing red nose.

### 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. . . .

### Stringing it Out

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

Explore the transformations and comment on what you find.