Hello! I’ve started trying to make more sense of math lately. Here are some of the notes I made about:
- fun patterns in addition and subtraction
- a bit about the history of numbers and
- the etymology of math names/labels.
I wrote these mostly for myself, but figured others might find them useful — I’ll try and make the next batch neater and more comprehensible for others to read :)
Note: “commutative” in this context means you can swap the numbers around (so in the above, swapping x with y) and the result would still be the same.
Just in case anyone needs the notes/translations for any of the words above:
- Sum: the result produced when numbers are added together
- Consecutive: one after another (so 8 and 9 are consecutive, but 3 and 9 aren’t)
- Squared: a number multiplied by itself. Shorthand for “to the power of 2”. so 4 squared is 4 x 4, which is 16. It isn’t two “instances” of four (which is 8).
- Gosh I hope this is making sense to everyone
- Integer: a number which is not a fraction or a decimal; in other words, a whole number.
Bam, that’s my first batch of math notes for you. Finding fun in the things you’re learning is so important to continuing, which is why I didn’t necessarily include *the most useful notes* but rather *the information I found the most entertaining*. As time goes on and I am able to Math Better, perhaps I’ll make more coherent things that are fully intended to teach, rather than to simply be a fun tidbit?
❤
Crystal
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Transcript
Hello! I’ve started trying to make more sense of math lately. Here are some of the notes I made about:
- fun patterns in addition and subtraction
- a bit about the history of numbers and
- the etymology of math names/labels.
I wrote these mostly for myself, but figured others might find them useful — I’ll try and make the next batch neater and more comprehensible for others to read :)
Math is an Artificial Language
Image Description: a sum showing x - y = thing.
The number on the left of the operator (so the x in the diagram) is called the “minuend”, meaning “to diminish, to get smaller”. The number on the right of the operator (the y in the diagram) is the “subtrahend”, meaning “to be taken away”.
This is important because subtraction is not commutative like addition.
Note: “commutative” in this context means you can swap the numbers around (so in the above, swapping x with y) and the result would still be the same.
In addition, 8 + 9 is the same as 9 + 8. This is commutative. In subtraction, 8 – 9 is not the same as 9 – 8. However, we can play with numbers a bit. A - B might not be the same as B - A, but A - B is the same as A + (-B).
Example 1:
3 – 4 = -1
3 + (-4) = -1
so 3 – 4 and 3 + (-4) are the same.
Example 2:
5 – 3 = 2
5 + (-3) = 2
so 5 – 3 and 5 + (-3) are the same.
Patterns!
The sum of consecutive positive odd numbers (starting from 1) equals the amount of odd numbers, squared.
1 + 3 = 4
There are two integers in the above sum. 2² is 4.
1 + 3 + 5 = 9
There are 3 integers in the above sum. 3² is 9.
1 + 3 + 5 + 7 = 16.
There are 4 integers in the above sum. 4² is 16!
Just in case anyone needs the notes/translations for any of the words above:
- Sum: the result produced when numbers are added together
- Consecutive: one after another (so 8 and 9 are consecutive, but 3 and 9 aren’t)
- Squared: a number multiplied by itself. Shorthand for “to the power of 2”. so 4 squared is 4 x 4, which is 16. It isn’t two “instances” of four (which is 8).
- Gosh I hope this is making sense to everyone
- Integer: a number which is not a fraction or a decimal; in other words, a whole number.
Sooo without calculating it, what’s 9² - 8²?
2² = 2 x 2. If you imagine (or draw) a 2 x 2 grid (in other words, a visualisation of 2²), you have 2 blocks x 2 blocks (so 4 blocks all up).
3² is a grid which is 3 blocks x 3 blocks. The 2 x 2 grid will fit into the 3 x 3 block with one row to spare horizontally and vertically. In other words, a row of 3 blocks and a row of 2 blocks = 5 blocks all up.
So 3² — 2² = 5.
This is likely confusing without trying it out yourself.
Final Notes
Why is this = the equals sign?
Greater than (>) and less than (<) used to be two separate sticks. Equals was the sign in between greater than and less than. Over time, greater than and less than were fused into symbols made of one bent line, while equals remained two separate lines.
The roman numeral for 10 is X.
But why?
People used to draw bundles of 10 things and then put a cross over it so you’d know the bundle of 10 was done. Over time, they dropped the drawings but kept the X. X = 10.
Why is the Roman numeral for 5 V? Because half of 10 is 5 and half of X is V :)
Bam, that’s my first batch of math notes for you. Finding fun in the things you’re learning is so important to continuing, which is why I didn’t necessarily include *the most useful notes* but rather *the information I found the most entertaining*. As time goes on and I am able to Math Better, perhaps I’ll make more coherent things that are fully intended to teach, rather than to simply be a fun tidbit?
❤
Crystal
