Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two...
Transcript of Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two...
![Page 1: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/1.jpg)
![Page 2: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/2.jpg)
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.
![Page 3: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/3.jpg)
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
![Page 4: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/4.jpg)
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
![Page 5: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/5.jpg)
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
![Page 6: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/6.jpg)
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
![Page 7: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/7.jpg)
YS NC Oct 2020
By changing what you actually draw or shade you can make the pattern look
different.
Examples
![Page 8: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/8.jpg)
YS NC Oct 2020
Vesica Piscis - Calculations
▪ Can you see any other lengths you can label in
this diagram?
radius
![Page 9: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/9.jpg)
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
![Page 10: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/10.jpg)
YS NC Oct 2020
▪ Now calculate the height of the triangle
▪ What about the Vesical Piscis ?
Using this equilateral triangle
![Page 11: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/11.jpg)
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?
![Page 12: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/12.jpg)
YS NC Oct 2020
▪ Unpick the 3D diagram
▪ Calculate the length AG then AF
▪ What do you notice ?
![Page 13: Geometry and Circles · 2020. 11. 6. · Vesica Piscis The construction starts by drawing two overlapping circles with the same radius. We will explore the relationship between the](https://reader035.fdocuments.in/reader035/viewer/2022070211/6100a1070596860e8b639bc6/html5/thumbnails/13.jpg)
YS NC Oct 2020