20a   visualization exercises1
Association creates meaning

Meaning changes with point of
view.
20a   visualization exercises1
Parallel lines that finally meet.
Ball balancing a seal.
Close-up of pig looking at book titles in a library.
Close-up of Count Dracula flossing
Dust cloud left by
the Road Runner

Fresh bubble
gum drooping
from under a
chair
Cut off each corner of a square, as far as the midpoints of the
edges. What shape is left over?

How many regular geometric shapes will the four corners
make if assembled?
How many edges does a cube have?

Cut off the corners of an equilateral triangle as far as
the midpoints of its edges. What is left over?
A tetrahedron is a pyramid with a triangular base.
How many faces does it have? How many edges?
Imagine a wire is shaped to go up one inch, right one inch,
back one inch, up one inch, right one inch, back one inch, ....
What does it look like?
Rotate the same object 90 degrees, clockwise, what does it
look like?
Can you draw the above figure as if it were standing on the
blackened side, with the edge AB standing perpendicular to it?
Can you draw the above figure as if it were standing on the
blackened side, with the edge AB standing perpendicular to it?
Can you draw the above figure so the viewer can see the object
three dimensionally (so all three sides are shown)?
Does it look anything like this?
Can you draw the above figure so the viewer can see the object
three dimensionally (so all three sides are shown)?
Does it look anything like this?
Can you draw the above figure so the viewer can see the object
three dimensionally (so all three sides are shown)?
Does it look anything like this?
Cut the cake so that it makes eight
equal pieces using only three cuts.
Change your point of viewof view to see the
Change your point to see the
cake’s three three dimensions, and then…
cake’s dimensions, and then…

Cut 1
Cut 2
Cut 3
(splits the quarters)
Glasses….
Arrange things so that the glasses alternate – filled
and empty – by moving only one glass.
Glasses….
By moving only one glass to fill an empty
one, we complete the task.
Looking beyond the obvious, dismissing
assumptions….finding creative solutions.
So what’s the answer?
20a   visualization exercises1

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20a visualization exercises1

  • 2. Association creates meaning Meaning changes with point of view.
  • 4. Parallel lines that finally meet.
  • 6. Close-up of pig looking at book titles in a library.
  • 7. Close-up of Count Dracula flossing
  • 8. Dust cloud left by the Road Runner Fresh bubble gum drooping from under a chair
  • 9. Cut off each corner of a square, as far as the midpoints of the edges. What shape is left over? How many regular geometric shapes will the four corners make if assembled?
  • 10. How many edges does a cube have? Cut off the corners of an equilateral triangle as far as the midpoints of its edges. What is left over? A tetrahedron is a pyramid with a triangular base. How many faces does it have? How many edges?
  • 11. Imagine a wire is shaped to go up one inch, right one inch, back one inch, up one inch, right one inch, back one inch, .... What does it look like? Rotate the same object 90 degrees, clockwise, what does it look like?
  • 12. Can you draw the above figure as if it were standing on the blackened side, with the edge AB standing perpendicular to it?
  • 13. Can you draw the above figure as if it were standing on the blackened side, with the edge AB standing perpendicular to it?
  • 14. Can you draw the above figure so the viewer can see the object three dimensionally (so all three sides are shown)?
  • 15. Does it look anything like this?
  • 16. Can you draw the above figure so the viewer can see the object three dimensionally (so all three sides are shown)?
  • 17. Does it look anything like this?
  • 18. Can you draw the above figure so the viewer can see the object three dimensionally (so all three sides are shown)?
  • 19. Does it look anything like this?
  • 20. Cut the cake so that it makes eight equal pieces using only three cuts.
  • 21. Change your point of viewof view to see the Change your point to see the cake’s three three dimensions, and then… cake’s dimensions, and then… Cut 1 Cut 2 Cut 3 (splits the quarters)
  • 22. Glasses…. Arrange things so that the glasses alternate – filled and empty – by moving only one glass.
  • 23. Glasses…. By moving only one glass to fill an empty one, we complete the task. Looking beyond the obvious, dismissing assumptions….finding creative solutions.
  • 24. So what’s the answer?

Editor's Notes