Why Do We Disagree With Kepler?
4. Do you agree with Kepler? Explain. Yes I agree with Kepler because of the definition of matter. Which is anything that has mass and takes up space. So any object that has matter can be considered geometry.
5. In grade school teachers often have geometry scavenger hunts; they ask students to find as many triangles, rectangles, and circles as they can. Spend a few minutes doing this. Write down all of the basic shapes that you find. Let’s see what happens if we are not confined to thinking of geometry as something motivated by basic shapes. How about a snowflake?
• The door, TV, cup, light bulb, and dresser.
• I think a snowflake would be considered a part of geometry because it is combined with different shapes. 6. Most of us have …show more content…
made paper snowflakes by folding paper and then cutting it with scissors. Do so.
7. The snowflake you made earlier, is it six-cornered and does it exhibit six-fold symmetry, like the snowflakes that fall from the sky? If not, try again, being more thoughtful about your approach so you can make a six-cornered, symmetric snowflake.
8. What difficulties did you encounter in trying to create a six-cornered snowflake? Explain.
I encountered many difficulties trying to create this snowflake. I could not get the folding right for it to have six corners.
9. Many snowflakes that one finds hanging in elementary schools during the winter are not six-cornered. What do you think about this?
I think because teachers are limited on time they just make any kind of snowflakes not worrying if they are six-cornered. One thing teachers can do is explain to the students when they create the snowflakes is how real crystals have six-corners.
10. Take several of your spheres. Lay them on a flat surface. How can you pack them so they take up the least space? Can you explain why you think this packing is the most efficient? When I packed the spheres I packed them in a triangular shape and then a rectangular shape. I packed them by putting each sphere side by side on different rows. I think the triangular shape took up the least space.
11.
The goal now is to stack the spheres so that they rise vertically more than one layer. Add several more spheres to your collection and see if you can determine how to stack them so they take up the least space. Describe your stacking. Can you explain why you think this packing is the most efficient? Stacking the spheres was hard to do but I found that stacking them in a triangular shape was the most efficient when doing multiple layers. I stacked them layer by layer and it was difficult to get each layer to keep from falling at first.
12. Name some spherical objects that you have seen stacked. Is this stacking essentially the same as the one that you found? Explain. An example of a spherical object that I have seen stacked would be oranges at the store. They were stacked in a triangular shape.
13. Let’s continue to try to break free of the confines of basic shape geometry. Spend some time searching for things in the world around you that do not contain basic shapes, but rather more complicated, interesting geometric shapes, especially if these things do not have exact geometric names. Keep a list of the interesting things you have found.
• Windows at churches, paintings, cars, airplanes, roads, light fixtures, and jewelry.
14. Compare your new list with your earlier basic shapes list. What do you notice? Contrast what you have found with the Mandelbrot quote
above.
The list I made earlier was just basic shapes that anyone could see. The second list I made consisted of items that a person would have to look more in depth to see the actual shape.
15. Return to your list in Investigation 13. Choose a few objects on your list that are interesting. Despite not containing basic geometric shapes, are there shapes (e.g. curves, arcs, contours, faces, portrusions, angles) that are interesting? What are some of the features of the surface of your objects? Describe the relative sizes and scales of your objects and/or various components of your objects. Paintings can consist of many different shapes. They come in different shapes and sizes depending on what painting you are looking at. Another object I pointed out was a road. Because roads come in many different forms. You have some roads that are circular such as a roundabout and you also have roads with deep curves.
5. In grade school teachers often have geometry scavenger hunts; they ask students to find as many triangles, rectangles, and circles as they can. Spend a few minutes doing this. Write down all of the basic shapes that you find. Let’s see what happens if we are not confined to thinking of geometry as something motivated by basic shapes. How about a snowflake?
• The door, TV, cup, light bulb, and dresser.
• I think a snowflake would be considered a part of geometry because it is combined with different shapes. 6. Most of us have …show more content…
made paper snowflakes by folding paper and then cutting it with scissors. Do so.
7. The snowflake you made earlier, is it six-cornered and does it exhibit six-fold symmetry, like the snowflakes that fall from the sky? If not, try again, being more thoughtful about your approach so you can make a six-cornered, symmetric snowflake.
8. What difficulties did you encounter in trying to create a six-cornered snowflake? Explain.
I encountered many difficulties trying to create this snowflake. I could not get the folding right for it to have six corners.
9. Many snowflakes that one finds hanging in elementary schools during the winter are not six-cornered. What do you think about this?
I think because teachers are limited on time they just make any kind of snowflakes not worrying if they are six-cornered. One thing teachers can do is explain to the students when they create the snowflakes is how real crystals have six-corners.
10. Take several of your spheres. Lay them on a flat surface. How can you pack them so they take up the least space? Can you explain why you think this packing is the most efficient? When I packed the spheres I packed them in a triangular shape and then a rectangular shape. I packed them by putting each sphere side by side on different rows. I think the triangular shape took up the least space.
11.
The goal now is to stack the spheres so that they rise vertically more than one layer. Add several more spheres to your collection and see if you can determine how to stack them so they take up the least space. Describe your stacking. Can you explain why you think this packing is the most efficient? Stacking the spheres was hard to do but I found that stacking them in a triangular shape was the most efficient when doing multiple layers. I stacked them layer by layer and it was difficult to get each layer to keep from falling at first.
12. Name some spherical objects that you have seen stacked. Is this stacking essentially the same as the one that you found? Explain. An example of a spherical object that I have seen stacked would be oranges at the store. They were stacked in a triangular shape.
13. Let’s continue to try to break free of the confines of basic shape geometry. Spend some time searching for things in the world around you that do not contain basic shapes, but rather more complicated, interesting geometric shapes, especially if these things do not have exact geometric names. Keep a list of the interesting things you have found.
• Windows at churches, paintings, cars, airplanes, roads, light fixtures, and jewelry.
14. Compare your new list with your earlier basic shapes list. What do you notice? Contrast what you have found with the Mandelbrot quote
above.
The list I made earlier was just basic shapes that anyone could see. The second list I made consisted of items that a person would have to look more in depth to see the actual shape.
15. Return to your list in Investigation 13. Choose a few objects on your list that are interesting. Despite not containing basic geometric shapes, are there shapes (e.g. curves, arcs, contours, faces, portrusions, angles) that are interesting? What are some of the features of the surface of your objects? Describe the relative sizes and scales of your objects and/or various components of your objects. Paintings can consist of many different shapes. They come in different shapes and sizes depending on what painting you are looking at. Another object I pointed out was a road. Because roads come in many different forms. You have some roads that are circular such as a roundabout and you also have roads with deep curves.