Thanks for your work in keeping up RubyQuiz! My spare thinking time has been taken up by other work lately, but this one's simple enough that I feel fairly confident in typing up this solution while away from the nearest computer with a Ruby interpreter installed (browser Ruby didn't work for testing).

As a competition-loving math student, for me the obvious way to calculate the area of a triangle is Hero's formula:

class Vector

def distance(oth)

Math.sqrt(to_a.zip(oth.to_a).inject(0){|s,(a,b)|s+(a-b)**2})

end

end

class Triangle

def area

ab = @a.distance(@b)

bc = @b.distance(@c)

ac = @a.distance(@c)

s = (ab+bc+ac)/2

Math.sqrt(s*(s-ab)*(s-bc)*(s-ac))

end

end

## ···

----- Original Message ----

From: Matthew Moss <matthew.moss@gmail.com>

To: ruby-talk ML <ruby-talk@ruby-lang.org>

Sent: Saturday, April 19, 2008 11:39:34 AM

Subject: [QUIZ] Triangle Area (#160)

Apologies for the latest... Some busy stuff this week in "real life."

In light of that, I've kept this quiz simple: you only need implement

one function. I do provide brief descriptions of a few possible

techniques, but don't feel you need to do them all! Just pick one that

sounds interesting to you...

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3. Enjoy!

Suggestion: A [QUIZ] in the subject of emails about the problem

helps everyone on Ruby Talk follow the discussion. Please reply to

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Quiz #160

Triangle Area

Start with the following code for a Triangle class:

require 'matrix'

RANDOM_PT = lambda { Vector[rand(101)-50, rand(101)-50] }

class Triangle

def initialize(a, b, c)

@a, @b, @c = a, b, c

end

def Triangle.random(foo = RANDOM_PT)

Triangle.new(foo.call, foo.call, foo.call)

end

def [](i)

[@a, @b, @c][i]

end

def area

# Fill in this stub.

end

def inspect

"Triangle[#{@a}, #{@b}, #{@c}]"

end

alias to_s inspect

end

Your task this week is to write the code for the `area` method.

There are a few techniques that come to mind for determining (or

closely

estimating) the area of a triangle. You do not need to attempt all of

these;

just pick a technique that sounds fun and do implement it.

1. Determinant Method

It is possible to calculate the area of a triangle very simply using

just the

points as part of a matrix, and calculating the determinant of that

matrix.

See (http://mathforum.org/library/drmath/view/55063.html) for an

explanation

of the technique. This is quick and easy, so if you don't have much

time this

week, try this.

2. Monte Carlo Method

The Monte Carlo method first requires that you determine a bounding

area

(typically a box) that surrounds the test area (i.e. the triangle).

Then you

choose thousands of random points within the box, determining for each

point

whether it falls inside or outside the triangle.

Knowing the area of the box (an easier calculation) and the percentage

of

random points that fell inside the triangle, you can multiply those

two values

together to get the triangle's area.

3. Scan-Line Method

Imagine covering the triangle with horizontal bars of a certain

height, such

that each bar is only wide enough to hide the triangle underneath.

Knowing

the width and height of each bar (i.e. rectangle) lets you calculate

the area

of each, and summed together is an approximation of the triangle's

area.

(This is sometimes called a scan-line method, as you are examining

horizontal

slices of the subject, very much like a television scan line draws a

number of

horizontal slices of the picture.)

Each time the height of the bars are halved (and twice as many are

employed),

your estimate of the triangle's area will improve. Those familiar with

calculus

will recognize this as integration, as the height of each horizontal

slice

approaches zero.

4. Something else!

If none of these methods interest you, but you have with another

method to

estimate or determine exactly the triangle's area, please do!

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