teaching machines

Polar Graph

May 7, 2019 by Chris Johnson. Filed under public, twoville.

A year ago I decided to see if fifth graders could create shapes using polar coordinates. I bet myself that they could if we spent some time first traversing a polar grid, identifying the labels of the rings and the spokes. We didn’t think of them as angles and radii, because those semantics weren’t important to us. We just needed a mechanism for addressing locations on the grid.

I looked around on the internet for a polar graph paper that the students could draw on, but I wasn’t satisfied with my options. Few had labels, and I dreaded the prospect of adding them in by hand. An algorithm—not me—would be the appropriate laborer. To Twoville I turned and produced this graph:

  

    ringCount = 10
ringDelta = 10
spokeDelta = 10
outerRadius = ringCount * ringDelta

with viewport
  center = [0, 0]
  size = [outerRadius * 2 + 50, outerRadius * 2 + 50]

// Rings, small to big.
for i in 1..ringCount
  with circle()
    center = [0, 0]
    radius = i * ringDelta
    color = :black
    opacity = 0
    stroke.color = :black
    stroke.size = 0.2
    stroke.opacity = 1

// Spokes.
for i to 360 by spokeDelta
  degrees = i
  x = outerRadius * cos(degrees)
  y = outerRadius * sin(degrees)
  with text()
    position = [1.1 * x, 1.1 * y]
    color = :black
    message = degrees
    with rotate()
      pivot = [1.1 * x, 1.1 * y]
      degrees = degrees
  with line()
    vertex().position = [0, 0]
    vertex().position = [x, y]
    color = :black
    color = [0, 0, 0]
    size = 0.4

    
    
    
  
  
    

    ringCount = 10
ringDelta = 10
spokeDelta = 10
outerRadius = ringCount * ringDelta

with viewport
  center = [0, 0]
  size = [outerRadius * 2 + 50, outerRadius * 2 + 50]

// Rings, small to big.
for i in 1..ringCount
  with circle()
    center = [0, 0]
    radius = i * ringDelta
    color = :black
    opacity = 0
    stroke.color = :black
    stroke.size = 0.2
    stroke.opacity = 1

// Spokes.
for i to 360 by spokeDelta
  degrees = i
  x = outerRadius * cos(degrees)
  y = outerRadius * sin(degrees)
  with text()
    position = [1.1 * x, 1.1 * y]
    color = :black
    message = degrees
    with rotate()
      pivot = [1.1 * x, 1.1 * y]
      degrees = degrees
  with line()
    vertex().position = [0, 0]
    vertex().position = [x, y]
    color = :black
    color = [0, 0, 0]
    size = 0.4

  
  expand

Who needs a collection of 100 different versions of polar grid paper when you can have just one expressed parametrically?

The fifth graders managed just fine.