geometry and circles · 2020. 11. 6. · vesica piscis the construction starts by drawing two...
TRANSCRIPT
YS NC Oct 2020
Geometry and Circles
▪ Circles play an important role in being able to construct regular
polygons and our understanding of some geometric shapes.
▪ The ancient Greeks, in particular Euclid and Archimedes, were
very interested in circles.
▪ They found ways of drawing shapes just using straight edges
and compass – in fact it was a bit of a game to them as they
enjoyed the act of puzzling out how to do this.
YS NC Oct 2020
▪ One of the simplest polygons to draw with a compass and ruler is a hexagon.
▪ By leaving the circles in the diagram this is known as the ‘Seed of life’
▪ It is often depicted in sacred pictures or used as a basis for designs in Islamic
patterns.
▪ Can you see a hexagon in this shape? What other shapes can you see?
▪ It is formed from 6 circles all of which have the same radius
YS NC Oct 2020
Vesica Piscis
The construction starts by drawing two overlapping circles with
the same radius.
▪ We will explore the relationship between the red and blue lines, and
how this can be linked to a cube.
The centre overlap is called the Vesica Piscis
YS NC Oct 2020
Vesica Piscis - Calculations
▪ The two red dots show the centres of both circle.
▪ This means that the horizontal line is the radius
radius
YS NC Oct 2020
Constructing the Seed of Life
It is a good idea to use a pencil and to check that your compass is not easily
changed from it’s setting.
Now follow the instructions on this video
YS NC Oct 2020
By changing what you actually draw or shade you can make the pattern look
different.
Examples
YS NC Oct 2020
Vesica Piscis - Calculations
▪ Can you see any other lengths you can label in
this diagram?
radius
YS NC Oct 2020
▪ The red dots show the centre of the circles
▪ The purple dot, a point on its circumference
▪ This means the distance between these points
is the length of the radius
YS NC Oct 2020
▪ Now calculate the height of the triangle
▪ What about the Vesical Piscis ?
Using this equilateral triangle
YS NC Oct 2020
Calculation for diagonal of cube
▪ The red line, AF, is the diagonal of the cube with
side lengths 𝑥
▪ Can you calculate this length?
YS NC Oct 2020
▪ Unpick the 3D diagram
▪ Calculate the length AG then AF
▪ What do you notice ?
YS NC Oct 2020
