Unit 4- Desmos drawing and function families.
Link to Desmos project:
https://www.desmos.com/calculator/yqz6f8egny
I went about this project by experimenting a lot, at first I started out with just a circle, wanting to make some kind of a face, but by the end I had something completely different. When I just had the circle, I was trying to figure out how to put eyes in to make my face, but ended up making a cubic function instead that somehow went perfectly through my circle to make it look like yin yang. After a little bit more experimentation with different functions such as linear and quadratic, I made my final product, a melting yin yang ice cream cone. Throughout this project I needed help figuring out how to shade and make some of the functions, so my teacher was consulted along with some peers and parents.
Using Desmos for this project helped me to figure out functions because of repetition. Along the process of this project you had to use each function multiple times, meaning you had to figure out how to play with those functions and change their composition. This repetition of putting them in over and over again really helped to memorize the functions, just like how people study for tests. Specifically, I used a lot of circles and quadratic functions in my project, after a while, I sort of just stopped looking at the examples of circle / quadratic equations and had them memorized. This was super helpful because it saved me a bunch of time and also I will remember those in the future.
Link to Desmos project:
https://www.desmos.com/calculator/yqz6f8egny
I went about this project by experimenting a lot, at first I started out with just a circle, wanting to make some kind of a face, but by the end I had something completely different. When I just had the circle, I was trying to figure out how to put eyes in to make my face, but ended up making a cubic function instead that somehow went perfectly through my circle to make it look like yin yang. After a little bit more experimentation with different functions such as linear and quadratic, I made my final product, a melting yin yang ice cream cone. Throughout this project I needed help figuring out how to shade and make some of the functions, so my teacher was consulted along with some peers and parents.
Using Desmos for this project helped me to figure out functions because of repetition. Along the process of this project you had to use each function multiple times, meaning you had to figure out how to play with those functions and change their composition. This repetition of putting them in over and over again really helped to memorize the functions, just like how people study for tests. Specifically, I used a lot of circles and quadratic functions in my project, after a while, I sort of just stopped looking at the examples of circle / quadratic equations and had them memorized. This was super helpful because it saved me a bunch of time and also I will remember those in the future.
Manta TESSELLATIONS
Tessellations in life.
I started off my project with no idea what to do, looking at other peoples ideas and images from the internet I hoped to find some kind of an idea or at least make a connection to something I could do, but nothing seemed right. I made a tessellation, made it into some kind of ship, and then crumpled it and threw it away. Made another, tried to turn it into a penguin but same as before, crumpled it and threw it away. I was tired of not being happy with my tessellations, so finally I decided to make one and stick with it. After turning, twisting, and contorting my project I finally figured it looked like the aquatic sea creature called a mantaray.
I wanted to make a triangular tessellation out of a triangle, but after a large amount of time with no success, I finally settled on a rotational tessellation. Rotation is spinning the pattern around a point, rotating it. A rotation, or turn, occurs when an object is moved in a circular fashion around a central point which does not move. A good example of a rotation is one "wing" of a pinwheel which turns around the center point. Rotations always have a center, and an angle of rotation.
These are the steps that are needed to construct a triangular rotational tessellation:
Personally, I do not think math is art. There are mathematicians and there are artists, they have different names for a reason. Math has to do with the brain, it is about remembering, writing, solving and hypothesizing. Art comes from the heart, you can paint, draw, sketch what you feel, what you wish to put on the paper does not have to be well thought out. Jamie Condliffe, a writer said “By definition, art has no functions, so it cannot truly be art” (http://gizmodo.com/is-math-art)
Even the famous Mc Escher himself says “I believe that producing pictures, as I do, is almost solely a question of wanting so very much to do it well”. Notice how he calls them pictures, not equations. (http://www.mcescher.com/about/quotes/)
I started off my project with no idea what to do, looking at other peoples ideas and images from the internet I hoped to find some kind of an idea or at least make a connection to something I could do, but nothing seemed right. I made a tessellation, made it into some kind of ship, and then crumpled it and threw it away. Made another, tried to turn it into a penguin but same as before, crumpled it and threw it away. I was tired of not being happy with my tessellations, so finally I decided to make one and stick with it. After turning, twisting, and contorting my project I finally figured it looked like the aquatic sea creature called a mantaray.
I wanted to make a triangular tessellation out of a triangle, but after a large amount of time with no success, I finally settled on a rotational tessellation. Rotation is spinning the pattern around a point, rotating it. A rotation, or turn, occurs when an object is moved in a circular fashion around a central point which does not move. A good example of a rotation is one "wing" of a pinwheel which turns around the center point. Rotations always have a center, and an angle of rotation.
These are the steps that are needed to construct a triangular rotational tessellation:
- Construct an equilateral triangle and find the midpoints of each side
- Construct a random shape from vertex to midpoint outside of the triangle
- Trace the shape and rotate it 180 degrees
- Trace the entire shape and rotate it 120 degrees
- Cut trace and rotate
- Trace only the final shape, and rotate the tracing so it fits together
Personally, I do not think math is art. There are mathematicians and there are artists, they have different names for a reason. Math has to do with the brain, it is about remembering, writing, solving and hypothesizing. Art comes from the heart, you can paint, draw, sketch what you feel, what you wish to put on the paper does not have to be well thought out. Jamie Condliffe, a writer said “By definition, art has no functions, so it cannot truly be art” (http://gizmodo.com/is-math-art)
Even the famous Mc Escher himself says “I believe that producing pictures, as I do, is almost solely a question of wanting so very much to do it well”. Notice how he calls them pictures, not equations. (http://www.mcescher.com/about/quotes/)
Snail Trail
This picture is the "snail trail" geometry project, which was a collection of reflected colored points that were also rotated, to add to the symmetry, and translated. In this project we started out with 5 colored dots and eventually came out with a perfectly symmetrical design.
In this project i learned that working with colors and shapes is way more appealing to me than having to work with numbers and equations.....Maybe thats just because of the way I am or its a trait in the family.
In this project i learned that working with colors and shapes is way more appealing to me than having to work with numbers and equations.....Maybe thats just because of the way I am or its a trait in the family.
The burning tent lab.
A camper out for a hike is returning to her campsite. The shortest distance between her and her campsite is along a straight line, but as she approaches her campsite, she sees that her tent is on fire! She must run to the river to fill her canteen, and then run to her tent to put out the fire. What is the shortest path she can take?
A camper out for a hike is returning to her campsite. The shortest distance between her and her campsite is along a straight line, but as she approaches her campsite, she sees that her tent is on fire! She must run to the river to fill her canteen, and then run to her tent to put out the fire. What is the shortest path she can take?
Above is the Burning tent lab, but this is not an ideal picture.....This is a way that the camper would not want to go to go to the river and then the tent because it would take alot longer than the way that is in the picture below, and she would have much trouble with putting out the tentfire if she had to walk that far.
This location is the best way to get to the river then the tentfire without wasting any time, the geometry that leads me to this conclusion is that the angle is the closest that it will get to the other angle and that makes it a direct V to the tentfire, wasting as least time as possible.
I came to the conclusion about the first picture by looking at the paths that the camper would have to walk in order to get to the river and the tentfire, and much longer the distance would be to walk by measuring the angles and comparing them to the other angles.
I came to the conclusion about the first picture by looking at the paths that the camper would have to walk in order to get to the river and the tentfire, and much longer the distance would be to walk by measuring the angles and comparing them to the other angles.