4 Fibonacci numbers in nature An example of efficiency in nature.As each row of seeds in a sunflower or pine cone, or petals on a flower grows, it tries to put the maximum number in the smallest space.Fibonacci numbers are the whole numbers which express the golden ratio, which corresponds to the angle which maximises number of items in the smallest space.
5 Why are they called Fibonnaci numbers? Leonardo of Pisa, c1175 – c1250Liber Abaci, 1202, one of the first books to be published by a EuropeanOne of the first people to introduce the decimal number system into EuropeOn his travels saw the advantage of the Hindu-Arabic numbers compared to Roman numeralsRabbit problem – in the follow-up workAbout how maths is related to all kinds of things you’d never have thought of
6 Complete the table of Fibonacci numbers 123Complete the table of Fibonacci numbers
13 Some mathematical properties of Fibonacci numbers Report back at 13.45Try one or more of these.Try to find some general rule or pattern.Go high enough to see if your rules or patterns break down after a bit!Justify your answers if possible.Find the sum of the first 1, 2, 3, 4, … Fibonacci numbersAdd up F1, F1 + F3, F1 + F3 + F5, …Add up F2, F2 + F4, F2 + F4 + F6, …Divide each Fibonacci number by 11, ignoring any remainders.E WJ GS KH D
14 Are our bodies based on Fibonacci numbers? What do you notice?Find the ratio ofHeight (red) : Top of head to fingertips (blue)Top of head to fingertips (blue) : Top of head to elbows (green)Length of forearm (yellow) : length of hand (purple)Report back at 14.00
15 SpiralsUse the worksheet, and pencils, compasses and rulers, to create spirals based on Fibonacci numbersCompare your spirals with this nautilus shellDisplay of spirals at
16 What have Fibonacci numbers got to do with: Pascal’s triangleCoin combinationsBrick wallsRabbits eating lettucesCombine all that you want to say into one reportReport back at 14.53