Here are the first 7 words in the sheep talk sequence: A B AB BAB ABBAB BABABBAB ABBABBABABBAB
For the elephant’s trunk, start from the quarter circle of radius 3 and don’t draw the quarter circles with radii 1, 1, and 2.
Click here for the 30-minute Golden Maths Lesson Notes for Teachers
Click here for the 30-minute Golden Maths Lesson Worksheet.
The Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13,…
Tie a pentagon knot
If you draw a pentagon accurately can you find ratios of lengths equal to the Golden Ratio?
- Draw a square ABCD and take the length of the edges of the square as 1 unit.
- Extend the line DC.
- Mark M the midpoint of DC.
- Join MB.
- Draw an arc centre M radius MB cutting the extended line DC at point E.
- Mark E on DC so ME=MB
- Draw rectangle ADEF
ADEF is a Golden Rectangle.
- Calculate length MB
- Calculate lengths DE and CE
- Calculate the golden ratio DE/AD in surd form and to 3 decimal places.
Calculate the ratio BC/CE in surd form and to 3 decimal places.
What do you notice?
The two ratios DE/AD and BC/CE should be the same, the Golden Ratio.
The Last Supper by Salvador Dali (1955).
Notice the proportions of the rectangles in this painting. Also notice the pentagon. It is actually part of a dodecahedron. The Golden Ratio occurs in many ratios in a pentagon.
Do some research on the internet about the Golden Ratio in art.