Tessellation Project
Steps to creating Tessellation:
Step 1: I first constructed a square.
Step 2: Translated my design to the top of the square.
Step 3: Can you see what I have created?
Step 4: Tessellate!
Steps to creating Tessellation:
Step 1: I first constructed a square.
Step 2: Translated my design to the top of the square.
Step 3: Can you see what I have created?
Step 4: Tessellate!
My tessellation!
Where the Wild Designs Are
2. What polygons did you start with and how did you alter it (what transformations did you use)?
The polygon I originally started off with was a square. I began with a hand drawing of the squares and incorporated lines and created angles., I translated my shape into a an Excel spread sheet and used repetition of my tile. I made multiple Max’s and lined them up proportionately. The repetition of all the squares added up to 360 degrees. Using Excel allowed me to be very uniform and achieve uniform angles because the program requires the user to work with cells. I divided some cells to create the crown, but each part of this paper really stared with a small square. There is a lot of repetition of squares that form larger rectangles One place I used the concept of reflection was that the crown is in gold, and the night sky is dark blue, but these are really mirror images just in different colors.
3. What transformations describe how your pre-image tile moved to create your two image tiles?
The type of transformation I used the most in my project was sliding. I moved my design horizontally and vertically to create the rows of crowns and Max’s. I also used the concept of flipping to create the night sky and the crown. I have overlays and many squares. There are squares for the background that are different colors and squares of Max’s head.
In your opinion, are tessellations math or art.
4.
Tesselations are both math and art. Tesselations were common in ancient Greek and Roman architecture, and these cultures were known for mathematical advancements and their art. You can see these tessellations on the floors of some of their famous buildings. A lot of art uses repetition, so math is a part of a lot of forms of art. The way that tessellations are art is that they are beautiful and creative and have many different colors. They are math because the concepts of transformation like translations, sliding and rotations are used. Beyond being math or art, tessellations can be practical in different situations, such as floor designs, architecture, and tapestry and cloth designs. According to the article IAD’s Art Tessellations Page M. C. Escher happened to design many postage stamps, tapestry and cloth designs as well in a very creative way. Also, the page titled tessellations demonstrates every mathematical concept my class and I have discussed and learned throughout this project, but the page also shows all the creative and fascinating art that tessellations bring. These two pages demonstrated in my opinion show that tessellations are definitely math and art. Overall I feel that tessellations are definitely both math and art and that the art is more visible, but the mathematical concepts are hidden.
Sources
http://www.incredibleart.org/lessons/middle/tessell.htm
http://www.incredibleart.org/lessons/middle/tessell.htm
- What is the idea/theme behind your tessellation?
2. What polygons did you start with and how did you alter it (what transformations did you use)?
The polygon I originally started off with was a square. I began with a hand drawing of the squares and incorporated lines and created angles., I translated my shape into a an Excel spread sheet and used repetition of my tile. I made multiple Max’s and lined them up proportionately. The repetition of all the squares added up to 360 degrees. Using Excel allowed me to be very uniform and achieve uniform angles because the program requires the user to work with cells. I divided some cells to create the crown, but each part of this paper really stared with a small square. There is a lot of repetition of squares that form larger rectangles One place I used the concept of reflection was that the crown is in gold, and the night sky is dark blue, but these are really mirror images just in different colors.
3. What transformations describe how your pre-image tile moved to create your two image tiles?
The type of transformation I used the most in my project was sliding. I moved my design horizontally and vertically to create the rows of crowns and Max’s. I also used the concept of flipping to create the night sky and the crown. I have overlays and many squares. There are squares for the background that are different colors and squares of Max’s head.
In your opinion, are tessellations math or art.
4.
Tesselations are both math and art. Tesselations were common in ancient Greek and Roman architecture, and these cultures were known for mathematical advancements and their art. You can see these tessellations on the floors of some of their famous buildings. A lot of art uses repetition, so math is a part of a lot of forms of art. The way that tessellations are art is that they are beautiful and creative and have many different colors. They are math because the concepts of transformation like translations, sliding and rotations are used. Beyond being math or art, tessellations can be practical in different situations, such as floor designs, architecture, and tapestry and cloth designs. According to the article IAD’s Art Tessellations Page M. C. Escher happened to design many postage stamps, tapestry and cloth designs as well in a very creative way. Also, the page titled tessellations demonstrates every mathematical concept my class and I have discussed and learned throughout this project, but the page also shows all the creative and fascinating art that tessellations bring. These two pages demonstrated in my opinion show that tessellations are definitely math and art. Overall I feel that tessellations are definitely both math and art and that the art is more visible, but the mathematical concepts are hidden.
Sources
http://www.incredibleart.org/lessons/middle/tessell.htm
http://www.incredibleart.org/lessons/middle/tessell.htm
Burning Tent Lab
Q and A
1. Once you have the minimal path what appears to be true about the incoming and outgoing angles?
The angles appear to be the same when they are dragged.
2. Why is the segment from camper to tent fire the shortest path?
It is the shortest path because it has the least distance.
3. Where should point river be located in relation to the segment camper to tentfire and line AB so that the sum of the distances is minimized?
It should be located farther to the left so that the distance will be minimized.
1. Once you have the minimal path what appears to be true about the incoming and outgoing angles?
The angles appear to be the same when they are dragged.
2. Why is the segment from camper to tent fire the shortest path?
It is the shortest path because it has the least distance.
3. Where should point river be located in relation to the segment camper to tentfire and line AB so that the sum of the distances is minimized?
It should be located farther to the left so that the distance will be minimized.
Snail Trail Lab
Snail Trail Lab reflection Ethan Sullivan
9/22/14
Geometry P.1
To construct the reflective plane in the snail trail lab I started with creating a circle with point A in the center. Then later added b, c and d. I then constructed 3 lines through the center A. I would say the figure I have constructed has line symmetry and reflectional because if you took a mirror to the image it would look the same on both sides representing reflectional symmetry. This is also line symmetry because as simple as it sounds there are lines that go through it and to have line symmetry there has to be lines on the image. I thought this lab was overall interesting, but confusing and I would like to go back and refine this lab and learn more of the applied concepts in it and give it perhaps another try.
9/22/14
Geometry P.1
To construct the reflective plane in the snail trail lab I started with creating a circle with point A in the center. Then later added b, c and d. I then constructed 3 lines through the center A. I would say the figure I have constructed has line symmetry and reflectional because if you took a mirror to the image it would look the same on both sides representing reflectional symmetry. This is also line symmetry because as simple as it sounds there are lines that go through it and to have line symmetry there has to be lines on the image. I thought this lab was overall interesting, but confusing and I would like to go back and refine this lab and learn more of the applied concepts in it and give it perhaps another try.
Unit 2
Reflection
1.What has been the work you have been most proud of in this unit?
The work that I have been most proud of in the trigonometry unit has been my quiz 3 on basic trig because it was a big deal for me to succeed on the quiz because normally I do not. Also, this quiz helped me get my confidence level in geometry and with trigonometry up because sometimes all it takes is one grade or one little thing to build your confidence. From this quiz everybody including my self began to realize how much trigonometry will continue to be used throughout the rest of year in units and even the real world.
2. What skills are you developing in geometry/math?
In geometry and math I feel like I am developing problem solving abilities. Math has always been a hard class for me that really pushes me and with trigonometry and past units I have really been forced to dig deep to understand concepts. With math and geometry I feel like my ability to advocate for myself has gotten better because I have kept consistent all year with meeting with a tutor and coming in for help when needed. Math has pushed me quite a bit this year which had been a challenge, but also a good thing for me to think hard and work through challenges.
3. Choose one topic: similarity (ratios) or trigonometry. Explain what it is. Provide an example of how it is used in mathematics to solve problems. State an application of the topic in the adult world that interests you?
Trigonometry is a branch of math that studies relationships with lengths and angles in triangles. Based on our whole unit with studying trigonometry it is constantly used in mathematics to find missing lengths of triangles and other shapes. It is also used in our current area a lot to whenever there is an angle involved in finding the area. An application of trigonometry that interests me is in architecture. Architecture has recently been intriguing to me and having a good background in trigonometry is crucial with being an architect. In architecture you are always drawing out designs for things and it needs to be spot on with calculations of the area and lengths because if it is not your whole design could be a waste and it could throw everything completely off. Trigonometry is a very important thing to know and is always used in mathematics and has some very important important applications in the adult world in many valuable jobs.
Reflection
1.What has been the work you have been most proud of in this unit?
The work that I have been most proud of in the trigonometry unit has been my quiz 3 on basic trig because it was a big deal for me to succeed on the quiz because normally I do not. Also, this quiz helped me get my confidence level in geometry and with trigonometry up because sometimes all it takes is one grade or one little thing to build your confidence. From this quiz everybody including my self began to realize how much trigonometry will continue to be used throughout the rest of year in units and even the real world.
2. What skills are you developing in geometry/math?
In geometry and math I feel like I am developing problem solving abilities. Math has always been a hard class for me that really pushes me and with trigonometry and past units I have really been forced to dig deep to understand concepts. With math and geometry I feel like my ability to advocate for myself has gotten better because I have kept consistent all year with meeting with a tutor and coming in for help when needed. Math has pushed me quite a bit this year which had been a challenge, but also a good thing for me to think hard and work through challenges.
3. Choose one topic: similarity (ratios) or trigonometry. Explain what it is. Provide an example of how it is used in mathematics to solve problems. State an application of the topic in the adult world that interests you?
Trigonometry is a branch of math that studies relationships with lengths and angles in triangles. Based on our whole unit with studying trigonometry it is constantly used in mathematics to find missing lengths of triangles and other shapes. It is also used in our current area a lot to whenever there is an angle involved in finding the area. An application of trigonometry that interests me is in architecture. Architecture has recently been intriguing to me and having a good background in trigonometry is crucial with being an architect. In architecture you are always drawing out designs for things and it needs to be spot on with calculations of the area and lengths because if it is not your whole design could be a waste and it could throw everything completely off. Trigonometry is a very important thing to know and is always used in mathematics and has some very important important applications in the adult world in many valuable jobs.
Problems of the week (POW's)
Reflection:
Pow's this year in geometry have helped me really grow as a learner and in understanding geometry. POW's have also been a really creative way to learn geometry concepts because they really make you think and you can also have fun while figuring them out. POW's have especially taught me how to keep my work and information for them organized because it is crucial to have your work and information to keep your thinking process high.
POW 3 - Solar POW
Unit 3 Reflection
1. What content/skills have been most interesting to you?
A lot of the content on the POW was interesting to me with volume and surface area and volume which has been a lot of the content we have covered this year. What I found fascinating about volume and surface area was that it is used a lot in the real world for many things we are not aware of. Something else that struck me this unit was visualization because I feel like it really helped me on the POW and I felt like this would be a key skill for understanding things because it can really simplify things in math. This unit contained many valuable skills and content that I find very useful and engaging and that I feel like will help get through the rest of the year and will help me next year and in the future.
2. How have you grown mathematically?
I have always struggled when it comes to math and I felt very positively about this unit and gained some self confidence. The POW's really helped me grow mathematically as well because I understood them pretty well and they are what made me gain the most confidence with concepts in this unit. During the course of this unit it took a lot of problem solving and calculator work and I realized that this is super key in math and I need to develop these skills as fast as I can because it will help me tremendously as a mathematician. I really benefited from this unit and really gained a lot of self confidence which is key for me to be successful in math.
Unit 4- Desmos Drawing and Function Families
Copy and paste link into search engine to see the drawing https://www.desmos.com/calculator/mqq0b9dhsm