Geometry Art I

Review — the Sketch Pad arc 5 min

• pen down draws as the sprite moves. pen up stops drawing.
• set pen color to [#ff4fa3] and set pen size to (3) change the line.
• erase all wipes the Stage. stamp prints a copy of the sprite.

Quick-fire

The pen is down. The sprite is at x: 100, y: 0. This runs:

go to x: (0) y: (0)
pen up
go to x: (0) y: (100)
          

How many lines are on the Stage?

Today’s Topic 3 min

• An arrow sprite that draws where it points
• The 360 rule — the turn at each corner is 360 ÷ sides
• A My Block with two inputs: polygon (sides) (size) :: custom

Learning outcome

By the end of this lesson you will be able to:

1. Draw a square with move and turn.
2. Work out the turn for any regular shape.
3. Make one block that draws a shape with any number of sides.

Learnt — a block that draws any shape 28 min

1 · An arrow that draws

In Sketch Pad you moved the pen with the mouse. Today a script moves it. We use the Arrow1 sprite, because it shows which way it is facing. The next move (10) steps always goes the way the arrow points.

1. Add the Arrow1 sprite. Set its size to 45.
2. point in direction (90) makes it face right.
3. turn cw (90) degrees makes it face down.

2 · A square, by hand

when flag clicked
erase all
set pen size to (4)
set pen color to [#ff4fa3]
pen up
go to x: (-60) y: (80)
point in direction (90)
pen down
repeat (4)
  move (120) steps
  turn cw (90) degrees
  wait (0.5) seconds
end
            

3 · The 360 rule

A sprite that walks all the way round a shape and ends facing the same way has turned once, all the way round. That is 360 degrees. Share it between the corners:

Scratch can do the sum for you. Put an operator in the turn:

turn cw ((360) / (5)) degrees

turn cw ((360) / (sides)) degrees

4 · One block for every shape

1. My Blocks → Make a Block.
2. Type polygon.
3. Click Add an input and name it sides.
4. Click Add an input again and name it size. Click OK.
5. Build the stack below under the define hat. Drag the orange ovals out of the hat.

define polygon (sides) (size)
repeat (sides)
  move (size) steps
  turn cw ((360) / (sides)) degrees
  wait (0.1) seconds
end
            

set [sides v] to (5)
set [turn v] to ((360) / (sides))
polygon (sides) (50) :: custom
            

Basic — six shapes from one block 24 min

Start a new project.

Step 1 — the board and the arrow

1. Click the Stage, then Backdrops → Paint. Fill it with a dark blue.
2. Delete the cat. Add Arrow1 and set its size to 45.
3. Add the Pen extension from the button at the bottom left.

Step 2 — the block

1. Make a Block called polygon with two inputs, sides and size.
2. Build the four-block definition from the Learnt.

Step 3 — get ready to draw

1. when flag clicked, then erase all.
2. set pen size to (3) and a bright pen colour.
3. pen up, go to x: (-50) y: (110), point in direction (90), pen down.

Step 4 — the ladder

1. Make a variable called sides. Set it to 2.
2. Add repeat (6).
3. Inside: change [sides v] by (1), then polygon (sides) (60) :: custom.
4. Last inside the loop: change pen (color v) by (15).

define polygon (sides) (size)
repeat (sides)
  move (size) steps
  turn cw ((360) / (sides)) degrees
  wait (0.1) seconds
end

when flag clicked
erase all
set pen size to (3)
set pen color to [#ffd23f]
pen up
go to x: (-50) y: (110)
point in direction (90)
pen down
set [sides v] to (2)
repeat (6)
  change [sides v] by (1)
  polygon (sides) (60) :: custom
  change pen (color v) by (15)
end
            

A circle that is not a circle

Scratch has no circle block. Your polygon block can still draw one.

• Use only your polygon block.
• The shape should look round from across the room.

polygon (36) (10) :: custom

A house

A square with a triangle roof. Both come from your polygon block.

• The roof sits on top of the square, not inside it.
• The roof is as wide as the house.

pen up
go to x: (-60) y: (30)
point in direction (90)
pen down
polygon (4) (120) :: custom
pen up
go to x: (-60) y: (30)
point in direction (30)
pen down
polygon (3) (120) :: custom
            

The same amount of ink

Draw eight shapes from one corner. Every shape must use exactly 360 steps of line — no more, no less.

• Use these numbers of sides: 3, 4, 5, 6, 8, 9, 10 and 12. Keep them in a list.
• Show sides and size on the Stage.
• Work out each size with a sum, not by hand.

set [n v] to (0)
repeat (length of [shapes v])
  change [n v] by (1)
  set [sides v] to (item (n) of [shapes v])
  set [size v] to ((360) / (sides))
  pen up
  go to x: (-60) y: (105)
  point in direction (90)
  pen down
  polygon (sides) (size) :: custom
  change pen (color v) by (10)
end
            

A shape dial

Turn your project into a toy. The arrow keys change the shape.

• The green flag draws a 5-sided shape.
• The up arrow adds a side and draws again on a clean board. Down takes one away.
• The dial stops at 3 and at 12.
• Every shape fits on the Stage.

define draw it
erase all
set pen size to (4)
set pen color to [#ff4fa3]
change pen (color v) by ((sides) * (8))
pen up
go to x: (-40) y: (100)
point in direction (90)
pen down
polygon (sides) ((420) / (sides)) :: custom
pen up

when [up arrow v] key pressed
if <(sides) < (12)> then
  change [sides v] by (1)
  draw it :: custom
end
            

Summary 5 min

• The arrow draws the way it points. Turn it, then move it.
• Walking all the way round a shape turns you 360 degrees. Each corner turns 360 ÷ sides.
• polygon (sides) (size) :: custom is four blocks, and it draws every regular shape.
• A short wait lets you watch a shape being drawn.

Regular shape

A shape whose sides are all the same length and whose corners are all the same.

Turn

How far the arrow swings at a corner. For a regular shape it is 360 ÷ sides.

Input

A number you give a My Block when you use it, like the sides and the size.

Hand in

Save your project. Next lesson the arrow turns further at every corner — and a pentagon becomes a star.