Lesson 10 of 11

Track quiz

9 min

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Eight ideas, eight checks. The table comes first, so nothing has to be remembered cold.

What a solid is made of, and what a repeated rule leaves behind
Idea	How it goes
Faces, corners, edges	Flat faces. Corners where edges meet. Edges where two faces meet.
A net	A flat plan that folds up. One flat piece per face.
Nets that fail	Of 35 ways to join six squares, 11 close into a cube.
Views	Front, top and side. Each is a flat shape.
Prisms and pyramids	Prism on n sides: n + 2, 2n, 3n. Pyramid: n + 1, n + 1, 2n.
Sierpinski triangle	Triangles left: 1, 3, 9, 27. Three times more each step.
Koch snowflake	Sides: 3, 12, 48. Four times more each step.
Sierpinski carpet	Squares left: 1, 8, 64. Eight times more each step.

How many edges does a triangular prism have?

Tape flaps hold a paper box together. Are the flaps part of its net?

Yes, every flap is part of the net
No, a net is only the unfolded faces
Yes, but only the flaps on the top

Six squares are joined in a straight row. Does the row fold into a cube?

Yes, six squares is enough
No, squares 1 and 5 land on the same face
Yes, if you start from the middle

A cone stands on its round base. What does its front view look like?

A circle
A triangle
A rectangle

A prism has a 10-sided base. How many faces does it have?

The triangle rule is run 3 times. How many triangles are left?

A snowflake starts with 3 sides. How many sides are there after 2 steps?

How many squares are left in the carpet after step 2?

Part II, Chapter 4 is Exploring Some Geometric Themes. You have folded a cube and kept a rule going. Take both with you and see what the chapter does with them.

Next: Tales by Dots and Lines — the mean, found by balancing.

Reveal every answer to finish this lesson.

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