perspective
3-d anamorphic project
TRIG APPLICATION: FINDING HEIGHTS OF LIGH TPOLES, TELEPHONE POLES, AND MOUNTAINS.
tan20/1=H/30+X
H=(X+30)tan20 H=xtan20+30tan20 xtan18=xtan20+30tan20 xtan-xtan20=30tan20 xtan(tan18-tan20)=20tan20 x=(30tan20)/(tan18-tan20) H=(tan18)X(30tan20)/(tan18-tan20) H= 90.85 |
tan(11) = H/X tan(10) = H/X+40
xtan(11) = H (x+40) (tan 10) = H Xtan(11) = xtan(10) + 40 tan(10) Xtan(11) - xtan(10) = 40 tan(10) X(tan(11) - tan(10)) = 40 tan(10) X = 40 tan(10)/tan(11) - tan(10) H=6.88 |
tan(15) = H/X tan(18) = H/X+90
Xtan(15) = H (x+90) tan(18) Xtan(18) + 90tan(18) = H Xtan(15) = Xtan(18) + 90tan(18) Xtan(15) - Xtan(18) = 90tan(18) (X)tan(15) - tan(18) = 90tan(18) X = 90 tan(18)/tan(15) - tan(18) H = 90 tan(18)tan(15)/tan(15) - tan(18) H=28.9 |
hexaflexagon The design of my hexaflexagon uses rotational symmetry and does not use line reflection symmetry. You can tell this by looking at the picture to the right. Notice how the sides are made up of only solid colors, if I rotated the design 120 degrees it would appear to be the exact same. This is rotational symmetry.
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A feature of my hexaflexagon design that I like more than others is the fact that you could flip this thing inside and out and it will still retain its completely natural shape and basic design.
The symmetry refinements I would make to my design are pretty basic. I would spend more time on coloring the hexaflexagon so that it not only had rotational symmetry and line-reflection symmetry.
In doing this activity, I learned that I work better and produce higher quality stuff when I feel it actually has real life relevance. Obviously that wasn't the case here seeing as how i rushed through it and didn't do a great job.
The symmetry refinements I would make to my design are pretty basic. I would spend more time on coloring the hexaflexagon so that it not only had rotational symmetry and line-reflection symmetry.
In doing this activity, I learned that I work better and produce higher quality stuff when I feel it actually has real life relevance. Obviously that wasn't the case here seeing as how i rushed through it and didn't do a great job.
Snail trail geogebra lab
Some of the geometry concepts used in this design are both obvious and then not so obvious. An obvious concept is the concept of symmetry, if you look at each pattern, you will notice that that pattern is shared two more times. This design is symmetrical by three different ways. A not so obvious concept is that this entire design is based purely on circles. You will have to look a bit closer to realize this but without circles, it would be near impossible for this design to be symmetrical at all.
Doing this lab i realized that when working on something that involves a computer in general or something that is graphically pleasing, I more thoroughly enjoy doing it compared to normal class work
Doing this lab i realized that when working on something that involves a computer in general or something that is graphically pleasing, I more thoroughly enjoy doing it compared to normal class work
two rivers geogebra lab
There is a sewage treatment plant at the point where two rivers meet. You want to build a house near the two rivers (upstream from the sewage plant, naturally), but you want the house to be at least 5 miles from the sewage plant. You visit each of the rivers to go fishing about the same number of times but being lazy, you want to minimize the amount of walking you do. You want the sum of the distances from your house to the two rivers to be minimal, that is, the smallest distance.
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? In this exploration you will investigate the minimal two-part path that goes from a point to a line and then to another point.
The above image does NOT satisfy the problem requirements because the distance of the path from the camper to the burning tent is not at its smallest length.
The image shown above is representing the best path possible from the camper to the burning tent. It is the best possible path because you are as far away from one side as you can be without adding more distance to the other.