# Top 10 math mnemonics

If you study undergraduate medicine, mnemonics are almost indispensable - there is so much factual material to learn. I was never given any mnemonics in my time as a maths undegraduate. But Robert Israel just mentioned "iciacids" to help remember the important features when looking at a function plot Function - Main Features? I would certainly have forgotten some of them.

So maybe mnemonics are useful for maths too. Maybe also for tricky proofs? Or for areas knee-deep in definitions, like topology? Does anyone know of a source for math mnemonics? Eg a top 10 type website? Or a kind of successor to sci.math FAQs (although I do not remember any mnemonics there)? Or a book?

• I find "sin = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent" to be a useful mnemonic; there's no other way I could ever remember how to spell the name Sohcahtoa. – bof Sep 11 '14 at 10:22
• I can't even think of four that I've ever used... – rschwieb Sep 11 '14 at 10:22
• With a little practice, isn't it rather hard to forget about increasing/decreasing behavior and concavity? The critical and inflection points come naturally as boundaries for those behaviors. Iciacids does not seem like a particularly serious mnemonic. – rschwieb Sep 11 '14 at 10:36
• @Aditya Lucky you :) The team of world wide number theorists who have still not managed to understand Mochizuki's proof of the abc conjecture should enlist you! But you are right, it is usually the concepts that are hard. – almagest Sep 11 '14 at 19:34
• @Bungo My mnemonics for keeping those addition formulas straight were "$\sin(a-a)=0$" and "$\cos(a-a)=1=\cos^2a+\sin^2a$". – bof Oct 5 '14 at 11:01

I remember the equality $$\Gamma(\frac{1}{2}) = \pi^{\frac{1}{2}}$$ by writing $$\Gamma( \frac{1}{2}= \Pi^{\frac{1}{2}}$$ or $$\Gamma(^{\frac{1}{2}}= \Pi^{\frac{1}{2}}$$

• What?${}{}{}{}$ – Unit May 11 '16 at 21:10
• @Unit It works better handwritten. The pair of characters $\Gamma($ looks a bit like a capital $\Pi$. – Patrick Stevens Aug 7 '16 at 17:23

Mnemonics are vital to teaching and learning mathematics. They are often unique as many are number-based, and as a mathematics teacher, they are quite powerful tools to help students, colleagues and ourselves the mathematical concepts.

Several studies have been performed on the effectiveness of their use, such as in Effects of Mnemonic and prior knowledge instructional strategies on students' achievement in Mathematics (Akinsola and Odeyemi, 2014), that concluded the most effective form of mnemonic in mathematics are ones that link prior knowledge with new concepts.

Also, as most formula use algebraic terms, these could be used as the first letters to make a sentence, or as a word, as a memory trigger.

There are many resources for mathematical mnemonics online,mostly are for elementary and high school students, such as the Education World website, which has 36 examples on this site, mostly for basic skills; and OnlineMath Learning.com, which includes some trigonometry and algebra. A basic visual mnemonic is included in a presentation for quaternions.

• Trying to figure out if this is a spoof. Guess I will have to check the refs :) – almagest Oct 5 '14 at 16:23
• @almagest I assure you, it is not a 'spoof', did some research to put together the answer. – user180820 Oct 5 '14 at 16:24
• Do not misunderstand. I am a strong supporter of mnemonics. I use them extensively in history, medicine etc. But for some reason maths sticks in my mind more easily. Also, this site seems, on balance somewhat hostile to them. I will read your material carefully when I can get to a desktop. At the moment I am struggling with an iPhone 6+ interface. – almagest Oct 5 '14 at 18:19
• @almagest I am new at this site, so are not sure what topics are denegrated here. All I can offer is my research skills. – user180820 Oct 6 '14 at 2:11

There are a few at Wikipedia:

I've always liked this one on the contraction mapping theorem (also from Wikipedia, though it's no longer on the page):

If $M$'s a complete metric space/(Non-empty) it's always the case/That if $f$'s a contraction/Then under its action/Exactly one point of $M$ stays in place.

In the absence of suitable mnemonics, I highly recommend Anki for memorising stuff in general.

I remember the beginning digits of the square root of two by counting the number of letters in each of the following words, and the sentence describes the square root of two, too.

** I have a root of a two whose square is two. **

1 4 1 4 2 1 3 5 6 2 3

Here is the E E E rule for signs of permutations:

Even number of Even cycles makes an Even permutation.

Yes, the sign is $$(-1)^ {\sum_{c \textrm{ cycle}} (|c|-1) }$$, but I remember it better with the triple E rule.