Perspectives
3-d project
For this project, each student made their own 3-D image with the orthographic and isometric sketches. Each student made their net and figure. There were many different steps to making the final figure piece ant final net as you can see in my pictures below.
My Anamorphic 3-d drawing project
Determining heights
For this project we were learning how to correctly use trigonometric ratios. To do this the class went outside and found the heights of things like tops of mountains, light posts, and poles. H stands for the height and X stands for the remaining distance between the object being measured and the already measured distance.
South top of mountain
tan28/1=h/x tan19/1=h/(x+92)
xtan28=xtan19=92tan19
xtan19-xtan28=92tan19
x(tan28-tan19)=92tan19
x=92tan19/(tan28-tan19)
x=169.056
h=92tan19/(tan28-tan19)*tan28
h=89.889
tan28/1=h/x tan19/1=h/(x+92)
xtan28=xtan19=92tan19
xtan19-xtan28=92tan19
x(tan28-tan19)=92tan19
x=92tan19/(tan28-tan19)
x=169.056
h=92tan19/(tan28-tan19)*tan28
h=89.889
East telephone pole
tan10/1=h/x tan15/1=h/(x+80)
xtan10=xtan15+80tan15
xtan10-xtan15=80tan15
x(tan15-tan10)=80tan15
x=80tan15/(tan10-tan15)
x=153.960
h=80tan15/(tan10-tan15)*tan10/1
h=27.147
tan10/1=h/x tan15/1=h/(x+80)
xtan10=xtan15+80tan15
xtan10-xtan15=80tan15
x(tan15-tan10)=80tan15
x=80tan15/(tan10-tan15)
x=153.960
h=80tan15/(tan10-tan15)*tan10/1
h=27.147
West Light post
tan41/1=h/x tan10/1=h/(x+78)
xtan41=xtan10+78tan10
xtan41+xtan10=78tan10
x(tan41-tan10)=78tan10
x=78tan10/(tan41-tan10)
x=19.847
h=78tan10/(tan41-tan10)*tan41/1
h=17.253
tan41/1=h/x tan10/1=h/(x+78)
xtan41=xtan10+78tan10
xtan41+xtan10=78tan10
x(tan41-tan10)=78tan10
x=78tan10/(tan41-tan10)
x=19.847
h=78tan10/(tan41-tan10)*tan41/1
h=17.253
Hexaflexagon
In the hexaflexagon I made it shows how rotational symmetry and line reflections work. My design shows when one colored triangle is shown it is reflected over a line of reflection to show the same pattern of the colored triangle and another triangle. As you would flip through my hexaflexagon you would see the symmetry that was created using patterns that would be symmetrical to each other when it was being created.
Reflection
When I was making the hexaflexagon it was a bit difficult to try and imagine the piece being finished, and what the completed product would look like while you were trying to piece together the triangles, but after I did finish the hexaflexaon I saw how lines of symmetry and rotational symmetry work and how they look. This activity might look like its just a simple coloring activity, but to pull off a good looking hexaflexagon you needed to imagine the finished product in your mind and know what piece goes with what piece to show rotational symmetry and line reflections. I am most proud of my critical thinking and problem solving to pull of this symmetrical puzzle.
Reflection
When I was making the hexaflexagon it was a bit difficult to try and imagine the piece being finished, and what the completed product would look like while you were trying to piece together the triangles, but after I did finish the hexaflexaon I saw how lines of symmetry and rotational symmetry work and how they look. This activity might look like its just a simple coloring activity, but to pull off a good looking hexaflexagon you needed to imagine the finished product in your mind and know what piece goes with what piece to show rotational symmetry and line reflections. I am most proud of my critical thinking and problem solving to pull of this symmetrical puzzle.
Snail Train Graffiti Geogebra Lab
In the Snail-Trail lab we learned how reflected points over lines will always stay perfectly reflected even when you move them around. To create this lab we started out creating any sized circle, then had to split this circle equally into six pieces with lines. After our circle was done we plotted one point anywhere in one of the six spaces, then we reflected this point over one of our six lines. After that process was completed we had to get the reflected point from the pre-image onto another one of the six spots, then reflected the second point over the neighboring line and so forth until each point was reflected over the neighboring lines in all six spots. We then made each point a different color and made then so they can move around and see the path they leave when the pints are moved. After you moved one point each point would move to show that if you move one point they would all move and stay perfectly reflected and stay the same distance from each of the other points.
Reflection
During the process of creating this design I had learned that if there are equal sized pieces of the circle and you plotted a point in one of the pieces and reflected it equally into each of the pieces it is like they are all mirroring each other. I learned that if you move one of the six points they will all mirror they one point. I learned that reflected points will always move perfectly in sync with each other over the line of reflection.
In the Snail-Trail lab we learned how reflected points over lines will always stay perfectly reflected even when you move them around. To create this lab we started out creating any sized circle, then had to split this circle equally into six pieces with lines. After our circle was done we plotted one point anywhere in one of the six spaces, then we reflected this point over one of our six lines. After that process was completed we had to get the reflected point from the pre-image onto another one of the six spots, then reflected the second point over the neighboring line and so forth until each point was reflected over the neighboring lines in all six spots. We then made each point a different color and made then so they can move around and see the path they leave when the pints are moved. After you moved one point each point would move to show that if you move one point they would all move and stay perfectly reflected and stay the same distance from each of the other points.
Reflection
During the process of creating this design I had learned that if there are equal sized pieces of the circle and you plotted a point in one of the pieces and reflected it equally into each of the pieces it is like they are all mirroring each other. I learned that if you move one of the six points they will all mirror they one point. I learned that reflected points will always move perfectly in sync with each other over the line of reflection.
Two Rivers Geogebra Lab
The Geogebra lab given was to create a sewage treatment plant at the point where two rivers meet. The task was to build a house near the two rivers that was upstream from the sewage plant, but we needed the house to be at least 5 miles from the sewage plant. The house had to be equidistant to both of the rivers to go fishing about the same number of times but being the shortest distance. You needed to minimize the amount of walking you do. We needed the distances from your house to the two rivers to be as least as possible. Using GeoGebra we created a sketch following these instructions.
The picture above would not be correct because the distance from the House to point A on the West river and the distance from the House to point B on the East river is not equal to the shortest distance that is possible. The location meets the requirements that the house must be out of the way of the sewage plant, but does not meet the requirement for the shortest distance possible.
The picture above would not be correct because the distance from the House to point A on the West river and the distance from the House to point B on the East river is not equal to the shortest distance that is possible. The location meets the requirements that the house must be out of the way of the sewage plant, but does not meet the requirement for the shortest distance possible.
The picture above would be the correct way because the distance from the house to point A on the West river, and the distance from the house to point B on the East river makes the shortest distance. This location reaches the requirements that the house must be out of the sewage plant, and is also the shortest path possible.
The Burning Tent Geogebra Lab
Somebody was camping and decided to go out for a hike and now is returning to her campsite. The shortest distance between her and her campsite is along a straight line, but as she comes upon her campsite, she notices 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 distance she can take to get water then put out the fire? In this task you will investigate the minimal two-part distances that go from a point to a line and then to another point.
Somebody was camping and decided to go out for a hike and now is returning to her campsite. The shortest distance between her and her campsite is along a straight line, but as she comes upon her campsite, she notices 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 distance she can take to get water then put out the fire? In this task you will investigate the minimal two-part distances that go from a point to a line and then to another point.
The image above shows the location on the river where you would want to fill your bucket with water. This is the correct way because the incoming and outgoing angles are equal in this scenario, meaning this is the shortest distance from the camper to get to the river then to the fire. You would then want to fill your bucket with water at this location on the river because it is the shortest distance from the camper to go to the river to get water then back to the fire. This is because the incoming and outgoing angles are equal.
The image above shows the location on the river where you would not want to fill your bucket with water because it does not meet the requirements. It doesn't meet the requirements because it is far away from both the camper and the tent, meaning a lot more distance for the camper to run. It does not accomplish the shortest distance line from the camper to the river.You would not want to fill your bucket at this place because it is not the shortest distance from the camper to go to the river to get water then to the fire. This is because the incoming and outgoing angles are not equal.