If you follow me on Twitter, you might have noticed that I’m a fan of legal blogger David Allen Green – not because I always agree with him, but because even when I don’t, he sets out a clear and compelling case for why I should.

He’s famed for writing in one-sentence paragraphs, because there’s “no place to hide” – it forces him to distil his argument down to its absolute key points, avoiding Johnsonesque word salad.

So, I wondered, what can the world of legal writing tell us about mathematical communication?

IRAC

I stumbled on an interesting cheat-sheet by Izzy (theheartbeating), about a “problem-solving technique for legal issues1” called IRAC.

So what is it 2?

It stands for:

  • Issue
  • Rule
  • Analysis
  • Conclusion

That is:

  • State the problem you’re faced with
  • State the rule or rules you rely on in your answer
  • Write down how the rule applies to the problem
  • Clearly state your answer.

An example

Let’s try it, based on a Madas IYGB A-level question (it’s question 1 on this paper). I’ve already solved the question, and am now trying to communicate my solution clearly.

Issue

Here, I’m just going to paraphrase the question. A diagram wouldn’t go amiss.

Square ABCD has sides of length 2. Point M is the midpoint of CD. Points A, B and M lie on a circle. What is the radius of the circle?

Rule

I’m going to state the main rule I rely on in my solution.

The intersecting chord theorem states that if two chords of a circle, PQ and RS, meet at a point X inside the circle, then |PX||XQ|=|RX||XQ|.

Analysis

A run down of my reasoning, in one-word paragraphs.

  • Let MN be the diameter of the circle perpendicular to CD.
  • Let X be the point where MN meets AB.
  • We know that:
    • |AX|=|XB|=1, since the diameter bisects the chord
    • |MX|=2, since MX is the shortest distance between AB and CD
  • Applying the rule as |AX||XB|=|MX||XN|, we get (1)(1)=(2)|XN|
  • Thus |XN|=12
  • The length of the diameter is therefore 2+12=52.

Conclusion

And finally…

The radius of the circle is half of the diameter, or 54

I think that’s a clear and tidy way to present the solution to a question! In an exam, you may not have the time or inclination to go through the rigmarole, but exams aren’t proper maths. If you’re trying to communicate your thinking – to someone else, or to future-you – then taking the time to refine and express your thoughts clearly will pay off.

Footnotes:

1. I would say it’s as much a presentation technique, but tomatoes, edible berries of the plant Solanum lycopersicum.

2. For those of you who don’t want to read the sheet, for some reason