mathematical art a 40 point circle mapping a drawing to download and try from the mathematics...
TRANSCRIPT
![Page 1: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/1.jpg)
Mathematical Art
A 40 point circle mapping
A drawing to download and try from theMathematics Department @
www.knightswoodsecondary.org
n 7n + 10 (mod 40)
Click spacebar to continue
![Page 2: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/2.jpg)
Right click the circle image from our download web page and save it to your hard drive. Open the image (it’s a jpeg) in a graphics program (download IrfanView using the link on the maths web page if you don’t have a suitable graphics program). Print out an A4 (portrait) size copy of the image on your printer. Now just follow these instructions!
![Page 3: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/3.jpg)
n 7n + 10 (mod 40)
Write in the mapping here
Look at the table at the foot of your printout
Press spacebar when ready
![Page 4: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/4.jpg)
Look at the mapping closely
n 7n + 10 (mod 40)
For n = 1, you do 7 x 1 + 10 = 17
So 1 maps to 17
Press spacebar when ready
![Page 5: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/5.jpg)
The Analysis
n 7n + 10 (mod 40)
17
Fill in the answers in the table
Press spacebar when ready
![Page 6: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/6.jpg)
Now consider n = 2
n 7n + 10 (mod 40)
For n = 2, you do 7 x 2 + 10 = 24
So 2 maps to 24
Press spacebar when ready
![Page 7: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/7.jpg)
The Analysis
n 7n + 10 (mod 40)
17
Put this answer below the 2 in the table
24
Press spacebar when ready
![Page 8: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/8.jpg)
Now consider n = 3
n 7n + 10 (mod 40)
For n = 3, you do 7 x 3 + 10 = 31
So 3 maps to 31
Press spacebar when ready
![Page 9: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/9.jpg)
The Analysis
n 7n + 10 (mod 40)
17
Put this answer below the 3 in the table
24 31
Press spacebar when ready
![Page 10: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/10.jpg)
Now consider n = 4
n 7n + 10 (mod 40)
For n = 4, you do 7 x 4 + 10 = 38
So 4 maps to 38
Press spacebar when ready
![Page 11: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/11.jpg)
The Analysis
n 7n + 10 (mod 40)
17
Put this answer below the 4 in the table
24 31 38
Press spacebar when ready
![Page 12: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/12.jpg)
Now consider n = 5
n 7n + 10 (mod 40)
For n = 5, you do 7 x 5 + 10 = 45
45 is too big (there are only 40 numbers on our circle) so you must subtract the mod
number
45 - 40 = 5Press spacebar when ready
![Page 13: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/13.jpg)
The Analysis
n 7n + 10 (mod 40)
17
Put this answer below the 5 in the table
24 31 38 5
Press spacebar when ready
![Page 14: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/14.jpg)
Now complete the rest of the mapping for yourself
Carefully look for patterns which will help you
Press spacebar when ready
![Page 15: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/15.jpg)
The Analysis
Press spacebar to complete the table (try it yourself first)
n 7n + 10 (mod 40)
17 24 31 38 5 30
10
12 19 26 33 40 7 14 21 28 35 2 9 16
37 4 11 18 25 32 39 6 13 20 27 34 1 8 15 22 29 36
23
3
Press spacebar when ready
![Page 16: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/16.jpg)
Now look at the circle abovethe table
You are about to start the drawing
Make sure you use a long rulerand pencil
Press spacebar when ready
![Page 17: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/17.jpg)
The Analysis
The first mapping is 1 17
n 7n + 10 (mod 40)
17 24 31 38 5 30
10
12 19 26 33 40 7 14 21 28 35 2 9 16
37 4 11 18 25 32 39 6 13 20 27 34 1 8 15 22 29 36
23
3
Press spacebar when ready
![Page 18: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/18.jpg)
Join 1 to 17on the circle
Press spacebar when ready
![Page 19: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/19.jpg)
The Analysis
The next mapping is 2 24
n 7n + 10 (mod 40)
17 24 31 38 5 30
10
12 19 26 33 40 7 14 21 28 35 2 9 16
37 4 11 18 25 32 39 6 13 20 27 34 1 8 15 22 29 36
23
3
Score out as you draw lines
Press spacebar when ready
![Page 20: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/20.jpg)
Join 2 to 24on the circle
Press spacebar when ready
![Page 21: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/21.jpg)
The Analysis
The next mapping is 3 31
n 7n + 10 (mod 40)
17 24 31 38 5 30
10
12 19 26 33 40 7 14 21 28 35 2 9 16
37 4 11 18 25 32 39 6 13 20 27 34 1 8 15 22 29 36
23
3
Score out as you draw lines
Press spacebar when ready
![Page 22: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/22.jpg)
Join 3 to 31on the circle
Press spacebar when ready
![Page 23: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/23.jpg)
The Analysis
The next mapping is 4 38
n 7n + 10 (mod 40)
17 24 31 38 5 30
10
12 19 26 33 40 7 14 21 28 35 2 9 16
37 4 11 18 25 32 39 6 13 20 27 34 1 8 15 22 29 36
23
3
Score out as you draw lines
Press spacebar when ready
![Page 24: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/24.jpg)
Join 4 to 38on the circle
Press spacebar when ready
![Page 25: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/25.jpg)
The Analysis
The next mapping is 5 5
n 7n + 10 (mod 40)
17 24 31 38 5 30
10
12 19 26 33 40 7 14 21 28 35 2 9 16
37 4 11 18 25 32 39 6 13 20 27 34 1 8 15 22 29 36
23
3
Score out as you draw lines
Press spacebar when ready
![Page 26: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/26.jpg)
The Analysis
Since 5 joins to itself there is no line to draw.. Just score it out
n 7n + 10 (mod 40)
17 24 31 38 5 30
10
12 19 26 33 40 7 14 21 28 35 2 9 16
37 4 11 18 25 32 39 6 13 20 27 34 1 8 15 22 29 36
23
3
Press spacebar when ready
![Page 27: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/27.jpg)
Now complete the rest of the drawing for yourself
Be very careful not to make mistakes and be as neat as you
possibly can
Press spacebar when you have finished
Press spacebar when readyPress spacebar when ready
![Page 28: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/28.jpg)
Press spacebarto completethe drawing
Press spacebar when ready
![Page 29: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/29.jpg)
Can you see anylines of reflectionsymmetry?
Press spacebarto see symmetry
![Page 30: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/30.jpg)
Lets colour a shape
And reflect in lines of symmetryPress spacebar when ready
![Page 31: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/31.jpg)
Choose another shape
And reflect in lines of symmetryPress spacebar when ready
![Page 32: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/32.jpg)
Now, change of colour
Press spacebar when ready
![Page 33: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/33.jpg)
Another shape
Press spacebar when ready
![Page 34: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/34.jpg)
Keep using the samemethod
Press spacebar when ready
![Page 35: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/35.jpg)
You can choose yourown shapes
Press spacebar when ready
![Page 36: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/36.jpg)
Keep on colouring
You can extendlines outside the circle Press spacebar when ready
![Page 37: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/37.jpg)
Here’s the same trickagain
Now add somebackground Press spacebar when ready
![Page 38: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/38.jpg)
And bring up the colour
![Page 39: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/39.jpg)
Rotate and label
![Page 40: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/40.jpg)
![Page 41: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/41.jpg)
Mathematical Artn7n+10(mod40)Internet downloadMr Rybarczyk 2002
Press spacebar when ready
![Page 42: Mathematical Art A 40 point circle mapping A drawing to download and try from the Mathematics Department @ n 77n + 10](https://reader036.vdocuments.mx/reader036/viewer/2022070401/56649f1e5503460f94c36750/html5/thumbnails/42.jpg)
I hope you enjoyed this piece of Mathematical Art. Why not try another drawing for yourself. Just choose a different mapping, complete the table, do the drawing and colour in.
Good Luck!