Koch Snowflake area calculator

conundrum

ruby-1.9.2-p0 > require './koch_snowflake'
 => true 
ruby-1.9.2-p0 > k=KochSnowflake.new 5,514
 => #<KochSnowflake:0x97222e4 @iteration=514, @size=5> 
ruby-1.9.2-p0 > k.area
 => NaN 
ruby-1.9.2-p0 > k=KochSnowflake.new 5,513
 => #<KochSnowflake:0x977cc80 @iteration=513, @size=5> 
ruby-1.9.2-p0 > k.area
 => 16.168975852600433 

equilateral_triangle.rb

class EquilateralTriangle
  def initialize side
    @length_of_side = side
  end

  def angle
    2* Math::PI / 6.0
  end

  def height
    Math.atan(angle) * @length_of_side / 2.0
  end

  def area
    @length_of_side * height
  end
end

equilateral_triangle_spec.rb

require './equilateral_triangle'

describe EquilateralTriangle do
  before  {@triangle = EquilateralTriangle.new 10}

  it "should have a correct angle" do
    @triangle.angle.should == Math::PI * 2 / 6.0
  end

  it "should have a correct height" do
    @triangle.height.should == Math.atan(@triangle.angle) * 5
  end

  it "should have a correct area" do
    @triangle.area.should == @triangle.height * 10
  end
end

koch_snowflake.rb

require './equilateral_triangle'
class KochSnowflake
  def initialize size, iteration
    @iteration=iteration

    @size=size
  end

  def self.extra_triangles iteration
    #0 1 2  3
    #0 3 12 48
    case iteration
    when 0 then return 0
    when 1 then return 3
    else
      return KochSnowflake.extra_triangles(iteration-1)*4
    end
  end
  def area
    area = 0
    @iteration.times do |i|
      if i==0
        area += EquilateralTriangle.new(@size).area 
      else
        triangles = KochSnowflake.extra_triangles(i)
        area += EquilateralTriangle.new(@size/3.0**i).area * triangles
      end
    end
    area
  end
end

koch_snowflake_spec.rb

require './koch_snowflake'

describe KochSnowflake do
  context "in general" do
    context "calculating number extra triangles to add for" do
      it "1st iteration" do
        KochSnowflake.extra_triangles(0).should == 0   # 0 * 3
      end

      it "2nd iteration" do
        KochSnowflake.extra_triangles(1).should == 3    #= 1*3   = 2^0*3
      end
      it "3rd iteration" do
        KochSnowflake.extra_triangles(2).should == 12   #= 4*3   = 2^2*3
      end
      it "4th iteration" do
        KochSnowflake.extra_triangles(3).should == 48   #= 16*3  = 2^4*3
      end
      it "5th iteration" do
        KochSnowflake.extra_triangles(4).should == 32*6 # = 64*3 = 2^8*3
      end
    end
  end

  context "with an iteration of 1" do

    let(:koch) { KochSnowflake.new 10,1 }

    it "has an area equal to the triangle" do
      koch.area.should == EquilateralTriangle.new(10).area
    end
  end

  context "iteration of 2" do
    let(:koch) { KochSnowflake.new 10,2 }

    it "has an area of 1 triangle plus 3 triangles with a 3rd of the base" do
      large = EquilateralTriangle.new(10.0).area
      small = EquilateralTriangle.new(10.0/3.0).area
      koch.area.should == large + (small * 3.0)
    end

  end

  context "with an iteration of 3" do
    let(:koch) { KochSnowflake.new 10,3 }

    it "has the correct area" do
      large  = EquilateralTriangle.new(10.0).area
      medium = EquilateralTriangle.new(10.0/3.0).area
      small  = EquilateralTriangle.new(10.0/9.0).area

      koch.area.should == large + (medium * 3.0) + (small * 12.0)
    end
  end

  context "with a interation of 10" do
    let(:koch) { KochSnowflake.new 10,4 }

    it "has the correct area" do
      large  = EquilateralTriangle.new(10.0).area
      medium = EquilateralTriangle.new(10.0/3.0).area
      small  = EquilateralTriangle.new(10.0/9.0).area
      tiny   = EquilateralTriangle.new(10.0/27.0).area
      #0 1 2  3
      #0 3 12 48

      koch.area.should == large + (medium * 3.0) + (small * 12.0) + (tiny * 48.0)
    end
 
  end
end