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#MathsMonday
1917 (iii) - Terms included in denominator
My investigation into (alleged) changes in #Mathematics rules in 1917 started with claims that the number of terms included in the denominator of a #Math expression was changed in 1917 (though I've yet to find any actual evidence of this - let me know if you have a reference for it). Some mentioned Lennes' letter, yet his letter says nothing at all about this! For now, let's assume it's true and see what that would mean for #Maths...

1/7
#MathsMonday
1917 (ii) - Lennes' letter (Terms and operators)
I've seen many refer to https://www.jstor.org/stable/2972726 as a change in #Mathematics precedence rules, and yet nothing at all actually changed! It does show that 100 years ago though, even then there were people #LoudlyNotUnderstandingThings #Math terms and rules! 😂

On page 93 he says "it is agreed that each symbol applies only to the term immediately following it" which shows he understands #Maths Terms and Left Associativity...

1/6
#MathsMonday
1917 (part 1) - Left Associativity
I have seen many people who argue about this #Mathematics issue that refer to changes in 1917, and I started to research it this week. The #Maths change I thought was made, I have not been able to find any reference for it, and that is about /2(1+3) vs. /2*(1+3). Apparently in pre-1917 #Math the latter was also considered to be a single term (in the denominator) but now is 2 terms. If anyone has a reference for that then please let me know...

1/6
#MathsMonday
1917 (part 1) - Left Associativity
I have seen many people who argue about this #Mathematics issue that refer to changes in 1917, and I started to research it this week. The #Maths change I thought was made, I have not been able to find any reference for it, and that is about /2(1+3) vs. /2*(1+3). Apparently in pre-1917 #Math the latter was also considered to be a single term (in the denominator) but now is 2 terms. If anyone has a reference for that then please let me know...

1/7
This week for #MathsMonday we are going to debunk the "implicit multiplication" (IM) claims (and also look at the mnemonics). I say claims, because there is actually no such thing as IM in #Mathematics. I find invariably the people who say there is have forgotten The Distributive Law (TDL) and/or Terms, but most often both! As we have already seen, these are both rules of #Maths, taught in many #Math textbooks, so that right away debunks any claims that "there is no convention in Maths"...

@claudius @pixelcode @quincy
Yeah, I'm going to cover that in a forthcoming #MathsMonday post. I believe I did already say to you (I said it to someone!) to just ignore anyone who says "implicit multiplication"? There's a reason for that... in an upcoming post 🙂

But as I shared already, it's defined in a whole bunch of Year 7-8 Maths textbooks - they should try picking one up before saying "not defined"!

@claudius @quincy @pixelcode
BWAHAHAHA! I just looked at your screenshot. a/b/c already IS unambiguous - it's equal to a/bc (already planned to be covered in an upcoming #MathsMonday ).

@claudius @quincy @pixelcode
Yeah I only ever look specifically for textbook stuff - the spread of misinformation online is what led to the need for my thread to begin with!

Tip: if you ever see "implicit multiplication" (which is on Wikipedia for example) then just save yourself time and stop reading right there. I'm going to cover this in a forthcoming #MathsMonday post in the current thread (I keep it to bite-size chunks each week - just 3-4 posts at a time to cover one aspect).

1/1
#MathsMonday Order of operations thread index
#Mathematics #Maths #Math
Introduction https://dotnet.social/@SmartmanApps/110807192608472798
1 The Distributive Law #DontForgetDistribution https://dotnet.social/@SmartmanApps/110819283738912144
2 Terms #MathsIsNeverAmbiguous https://dotnet.social/@SmartmanApps/110846452267056791
3 Factorising<->The Distributive Law https://dotnet.social/@SmartmanApps/110886637077371439

Yet to come (in no particular order yet)...
"implicit multiplication", adding brackets, mnemonics, 1/2/3, #Calculators , how we #Teachers #Textbook #Authors could improve #Education , 1917, (more?)

@rodhilton
For a breakdown on why Google Maths is wrong - textbook references and all - see my #MathsMonday thread about order of operations https://dotnet.social/@SmartmanApps/110807192608472798

@denki @fortyseven @clement_la_baleine @schmutzie
2(2+2) is a single, factorised term, which must be expanded according to The Distributive Law. For full coverage of everything read my (still in progress) #MathsMonday thread on order of operations https://dotnet.social/@SmartmanApps/110807192608472798
TL;DR Google is wrong

Thank you to everyone who voted - a little surprising results. I had intended to talk about it in this week's #MathsMonday, but ran out of space just talking about the first point (those 500 characters come quick when you're writing posts!), but definitely next week or the week after I will, and will update here with the link when I do.

1/4 #MathsMonday
Now we'll tie the previous 2 #Math rules together and see why #Mathematics order of operations means #MathsIsNeverAmbiguous provided you #DontForgetDistribution

Start with 1, also the result of any number divided by itself, so let's write 8/8

We can factorise, and 8 is even, so let's take out a 2, 8/2(4)

We can rewrite the stuff in brackets without changing the answer, so let's write 8/2(1+3)

I started with 1,so we have to make sure the rules of #Maths get us back there...

#Mathematics #Maths #Math poll: negative numbers do/don't have square roots?

Curious about this for an upcoming #MathsMonday and would like to see some numbers. Note I don't want any #Teacher #Teachers or anyone in #Education answering - I know you know 🙂 - I'm curious about what people remember being taught from their school days, so only answers from those people please. And please no comments with/on answers! I don't want people to be influenced by that. Also please boost. #Poll

#MathsMonday week 2, Terms.
Simply put, in #Mathematics Terms are separated by operators and joined by brackets. The most common example is 2a=(2*a). This makes it simpler to write fractions. e.g. 1/2a rather than 1/(2*a). That also means 1/2a isn't mistaken as half a, which would actually be written as a/2. Notice in the latter that the a is to the left of the division, which means it's in the numerator, and vice-versa for the former (more about this aspect of #Maths #Math later, but first)...

My first milestone on #Mastodon Thank you to all who have followed me so far, regardless of whether it's for my #dotNet and #Tech content, my #Maths #Math #Mathematics content, or just some of the (semi)random stuff. 🙂 A while ago I saw there was a Mastodon document of Mathematicians with more than 100 followers, so that became a goal of mine ✅ The sudden jump in numbers you see last week was when I started my first #MathsMonday thread (which I'll be continuing later today)

@jeffhandley
Agreed, but as a #Maths teacher the thing I find more infuriating is all the e-calculators that give wrong answers to #math expressions. That in itself is infuriating, but then to rub salt in there are often posts by #developers saying "you don't need to know Maths to be a programmer!", which I find downright embarassing since apparently none of them can manage to write a calculator that gives correct answers! I'll be covering calculators in a future #MathsMonday post #Mathematics

@beforewisdom
As a #Mathematics teacher, I can tell you I have run into a whole BUNCH of people (especially on #Twitter ) who would rather believe #Google than a #Maths textbook I have quoted! They even quote #ChatGPT which isn't even programmed to do Maths!

P.S. Follow #MathsMonday (or me directly) for semi-regular posts on actual #math (not Google's (mis)understanding of it) 🙂

@scott Oh ok. Well, it literally is just "remindme" then, which makes it weird the distinction between "dm" or not. If only I can see it, then there's no difference! Thought it'd be a good way to set reminders for your followers as well. For example, in my case, about #MathsMonday post coming up next week.

RT @page_eco@twitter.com

The trefoil knot is the simplest nontrivial knot in topology (can't be untied without a cut).

It is famous as the Celtic Triquetra. It is also present on Thor's hammer, Mjölnir.

#mathsmonday

🐦🔗: https://twitter.com/page_eco/status/967914295777378305