Modular Stars
Modular Stars
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Complete the following activities:
1. It was mentioned in the lesson material that we would not be discussing six-pointed stars in the part about
continuous line stars. This was because if you use the algorithm you used for the other continuous line stars,
you cannot make a continuous line star with six points. Explain why it is not possible to make a continuous
line star with six points. Are there any other numbers that would have this same problem?
2. Explain why an asterisk type star can only be made with an even number of points.
3. On Geoge
a, use the regular polygon tool to make a regular decagon (10 sided polygon). Change the
labels on the points on the vertices to be the numbers 0-9 and use the hide tool to hide the polygon and its
edges so that only the points can be seen. Use these points to create every possible 10-pointed star. After
creating each different star, export it as a picture and paste it in your homework document. With each star
picture, tell which number was added repeatedly in mod 10 to make that star. If there was more than one
number that could be used to make the same star, tell all the numbers with the picture of that star.
4. On Geoge
a, draw a star that is created from three overlapping 5-pointed stars. To do this, you will need
to determine which number to add repeatedly mod 15 to get this design. As with the last activity, start by
using the regular polygon tool to make a regular 15 sided polygon. Change the labels on the points on the
vertices to be the numbers 0-14 and use the hide tool to hide the polygon and its edges so that only the
points can be seen. Make your star on these points, export it as a picture, and paste it into your homework
document. Tell which number or numbers could be added repeatedly mod 15 to make the star.
5. Using the method from the lesson of adding the same number repeatedly in modular arithmetic, could a
star be made from two different overlapping shapes? For example, could a 9 pointed star be created using
this method that was made from a hexagon overlapping a triangle? Consider and answer this question for
any number, not just 9. If the answer is "no" explain why and if the answer is "yes" use Geoge
a (in the
same manner as the earlier activities) to create the star, export it as a picture, and paste it into your
homework document then tell which number and modulus was used to make the star.