Start to explore ideas of Fibonacci numbers and the golden ratio by copying the picture and drawing this spiral which is made up of quarter circles. Watch this inspirational video.
Then create your own elephant. The numbers in the centres of the squares give the radii of the quarter circles that you need to draw. You could continue the spiral on and on using the Fibonacci numbers for the radii of the quarter circles.
For the elephant, don’t draw the quarter circles with radii 1, 1, and 2 and replace the quarter circle of radius 21 with a semicircle of radius 10.5
What do you notice about this sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21 … ?
Continue this sequence for the next 5 terms.
If you calculate the ratios of pairs of successive terms you get (to 3 decimal places) the sequence:
1, 2, 1.5, 1.667, 1.6, 1.625, 1.615, 1.619 … . Calculate the next 3 terms in this sequence.
Click here for the ELEPHANT DREAMING Inclusion and Home Learning Guide.
Click here for the ELEPHANT DREAMING worksheet
Click here to download the Notes for Teachers.
Thank you Jain for allowing us to use your Elephant Dreaming picture. See http://jain108.com