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Exploring Some Geometric Themes

What you see from where

A round tin is a cylinder. From above, it looks like a circle. From the side, it looks like a rectangle. A square pyramid has a square base and a point on top.

A square pyramid.
Step 1 of 4
  1. A square pyramid.
  2. From above: a square with lines to the middle.
  3. From the front: a triangle.
  4. From one side: a triangle too.

Rule: Look straight at the solid from one side. The flat shape you see is a view. Front view, top view and side view are three of them.

A cone has a round base and a point on top. A cuboid is a box with rectangle faces.

Four solids, and the flat shape each one makes
SolidFrom aboveFrom the frontFrom one side
CubeA squareA squareA square
Square pyramidA square with lines to the middleA triangleA triangle
CylinderA circleA rectangleA rectangle
ConeA circle with a dot in the middleA triangleA triangle

One view cannot tell you which solid it is. A cylinder and a cuboid can both show a rectangle. That is why we look from more than one side.

Slide Look from. Watch the flat shape change.

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This track

  1. 0 Start here
  2. 1 Faces, edges and corners
  3. 2 A flat plan that folds up
  4. 3 Six squares, and most plans do not fold
  5. 4 What you see from where
  6. 5 A relation hiding in the counts
  7. 6 A shape inside itself
  8. 7 What each stage really does
  9. 8 The carpet, and fractals around us
  10. 9 The big picture
  11. 10 Track quiz

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