Random facts catch us off guard in the best possible way. They’re unexpected or unusual bits of knowledge that can teach, delight and entertain us. These interesting facts aren’t just amusing pieces of information, they’re legitimately fascinating pieces information that will assist you to uncover the mysteries of mathematics.
”Just the facts, ma’am”
Sgt. Joe Friday, Dragnet
Why do we generally use the letter ‘X’ in an equation instead of another letter?
Were geniuses ever accused of cheating in school?
Why is there a dx after f(x) in an integral?
Why don’t teachers want us to divide zero by zero?
Why do we generally use the letter ‘X’ in an equation instead of another letter?
Because a French guy decided it should be that way, possibly because his printer ran out of letters.
Once, a French man wrote a book, and that French man was René Descartes. Besides Napoleon, he is arguably the most famous French person. He’s responsible for things like modern philosophy and the saying Cogito ergo sum (“I think, therefore I am”).
Another thing he’s responsible for – well, several things, really – is one of the greatest contributions to math not made by a Greek person. He needed to tell people about these things, so he wrote some books. He needed to make lots of copies of the books, so he got them printed. (The alternative, and the main method in Europe before Gutenberg invented the printing press, was to write everything out by hand, over and over again.)
In his book La Géométrie, Descartes uses x, y, and z to represent unknown quantities. We’re not completely sure why he did this – it may have just been because those letters come at the end of the alphabet – but according to one theory, it was because his printer had lots of extras of those letters.
Back then, printers weren’t machines; they were people who would take letters out of boxes and arrange them into giant stamps, which could then be used to print things on pieces of paper.
(Interesting side note: The smaller letters, which were used more, were kept in the bottom row of boxes to make them easier for the printer to access, so they were lower case letters. The capital letters, since they were used less, were kept in the top row, so they were upper case. This is where we get those terms from.)
In French, the letters X, Y, and Z are uncommon, so the printers were less likely to run out of them than any other letters (besides K). The theory says that Descartes chose them to represent unknown quantities not only because they come in order at the end of the alphabet, but also due to the printers’ advice.
Whether or not this is true, the first use of X, Y, and Z in this way is found in La Géométrie, a book that tied geometry and algebra together and contributed to the development of calculus.
There are also other theories that suggest it’s an abbreviation of the Greek xenos (“unknown”) or a Spanish abbreviation of the transliteration of the Arabic word al-shalan (see here), but there’s little evidence for either and it’s mostly speculation. The first appearance with evidence is La Géométrie.
Tay, Oscar. “Why do we generally use the letter ‘X’ in an equation instead of another letter? – Quora”. 2023. Quora. https://qr.ae/prulfN.
Were geniuses ever accused of cheating in school?
One of the greatest mathematical minds of all time was once considered a possible cheat. It is not hard to see why.
When Carl Friedrich Gauss was just three (in 1780) he corrected a maths problem his father had gotten wrong.
It was when he was just seven years old though that his genius led to a suspicion that he was a cheat.
The story goes that his teacher decided to have an easy hour-long class, so asked the kids to use their blackboards to determine what the answer would be if you added 1+2+3+4… all the way for all numbers up to +100.
At the end of the lesson most kids had scrawlings all over their blackboards, as the teacher anticipated. You can only imagine that most had the answer incorrect. It is not easy to manually add up so many numbers as a seven year old without making an error.
But when the teacher got to Gauss’ blackboard there was only one number 5,050.
This was the correct answer. And a stunned teacher must have assumed some cheating, but Gauss soon explained how he reached the answer.
Instead of adding up the numbers in order he added them up from the ends. It doesn’t matter after all which order the numbers are added, it should give the same answer.
So he added up 100+1, then 99+2, then 98+3 and as you will notice, if you add up all the pairs, you will have exactly 50 groups of 101 (5,050).
There was only one Gauss, whose genius only grew stronger over time.
Francis, Xanthi. “Were Geniuses Ever Accused Of Cheating In School?”. 2023. Quora. https://qr.ae/prbMJ0.
Why is there a dx after f(x) in an integral?
Interestingly, about 50 years ago, some educators decided to drop the dx but the idea was not accepted by many traditional maths enthusiasts.
I will explain where the “dx” actually comes from.
The sum of the areas of these strips gets closer and closer to the actual area under the curve. We can find this limit as follows:
Consider one strip greatly enlarged for clarity.
EDIT. Although the dx does not have any real purpose when performing an integral, it does tell us what to integrate with respect to! And when doing a substitution such as when letting u = sin(x) then du becomes cos(x) dx which certainly does play a part in the rest of the Integration!
“Why is there a dx after f(x) in an integral?” 2023. Quora. https://qr.ae/prbuXo.
Why don’t teachers want us to divide zero by zero? My math teacher just stopped and said, “Well, class, we’re changing the topic,” when I asked him.
I usually have a great time explaining this idea!
Lloyd, Philip. “Why don’t teachers want us to divide zero by zero? My math teacher just stopped and said, “Well, class, we’re changing the topic,” when I asked him.” 2023. Quora. https://qr.ae/prmsFF.
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Mathematical Mysteries 