3d point perspective labs-
1 point perspective
2 point perspective
3D objects
Different ways to visualize 3D objects.
3d anamorphic drawing-
Anamorphic drawing example:
Measuring tall things-
This is my Hexaflexagon. The side shown in the picture uses rotational symmetry.
When one triangle is rotated, it creates the next. My project also uses lines of
reflection. Each triangle is a reflection of its neighbor. The part of my Hexaflexagon that pleases me most is the side shown in the picture. The stripes on this side all match up perfectly and that makes me happy. To improve my project I would be more patient and make sure that my designs match up. This activity made me realize that I am not very patient with coloring.
When one triangle is rotated, it creates the next. My project also uses lines of
reflection. Each triangle is a reflection of its neighbor. The part of my Hexaflexagon that pleases me most is the side shown in the picture. The stripes on this side all match up perfectly and that makes me happy. To improve my project I would be more patient and make sure that my designs match up. This activity made me realize that I am not very patient with coloring.
SNAIL TRAIL GRAFFITI
The first thing we constructed was a circle. This creates the rotational symmetry when the trace is turned on. When the four points are spaced equally around the circle, the designs have lines of reflection. I learned that I enjoy making crazy colorful, symmetrical designs with my computer.
The first thing we constructed was a circle. This creates the rotational symmetry when the trace is turned on. When the four points are spaced equally around the circle, the designs have lines of reflection. I learned that I enjoy making crazy colorful, symmetrical designs with my computer.
We will model the following scenario in a Geogebra sketch. 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.
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.
This is not acceptable because the only two options of
where to put the house are either on the East River or on the West River.
This picture does show the shortest distances from the house to each river
but it does not show the shortest sum of the distances.
where to put the house are either on the East River or on the West River.
This picture does show the shortest distances from the house to each river
but it does not show the shortest sum of the distances.
The house must be in the middle of a river because to go fishing
you will only have to walk out the door and you will
be the furthest possible distance from the sewage
plant. To create the shortest sum of the
perpendiculars, the house must be on
one of the rivers.
you will only have to walk out the door and you will
be the furthest possible distance from the sewage
plant. To create the shortest sum of the
perpendiculars, the house must be on
one of the rivers.
BURNING TENT
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.
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.
If the incoming and outgoing are not
congruent, the distance will not be the
shortest because the lines from Camper
to River and River to Tentfire will not add
up to the shortest distance.
congruent, the distance will not be the
shortest because the lines from Camper
to River and River to Tentfire will not add
up to the shortest distance.
To have the shortest distance from the camper
to the river to the tent, the incoming and outgoing angles at point
River must be congruent.
Camper-River-Tentfire must be equal to Camper-Tentfire'
to the river to the tent, the incoming and outgoing angles at point
River must be congruent.
Camper-River-Tentfire must be equal to Camper-Tentfire'