Luca Pacioli and The Summa De Arithmetica

Luca Pacioli didn’t invent much mathematically, although he did apparently invent double-entry accounting and the Rule of 72, a rule of thumb for determining how quickly an investment will double in size.

What he did was write a big textbook summarising the state of mathematics at the end of the 15th century-for the first time, written in a local dialect rather than in Latin.This made is more widely accessible than most books of the time, and opened up mathematics to much wider audience.

It’s also significant for its notation- it used p. and m. in place of + and -, and R. in place of √¯, but is otherwise quite mathematically legible. He has a look at quartic equations ( summarising which ones he knows how the solve), and gives a method for approximating square roots. He also analyses several games of chance, anticipating Fermat and Pascal, although his analysis is off the mark.

A few years later, Pacioli worked with Leonardo da Vinci on a book called Da divina proportione, a study of the maths of proportion and perspective, including the golden ratio; I’m a bit jealous- don’t get me wrong, I love the illustrators I’m working with for this book: they’re brilliant, but they’re not Leonardo brilliant!

THE RULE OF 72

If you invest £100 at 2% interest, it takes about 36 years for your investment to double in size. If you invested it at 8% interest, it would take roughly nine years. In general, if you invest your money at n% interest, it takes about 72/n years to double it.

£100 invested at 2% = £200 in 36 years

£100 invested at 8% = £200 in 9 years

£x invested at n% = £2x in 72/n years

Pacioli most likely discovered this rule empirically ( to work it out algebraically needs logarithms, which he certainly didn’t have access to ), but it’s a remarkably accurate rule of thumb.

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