High School Triangle of Powers: Revolutionary Math Notation

[fresh_42]

Oh no its the all seeing $\pi$
I'll raise you one $\prod$

I assume in memoriam, Cledus. But Bandit's name is written with a $P$.

 

[jedishrfu]

Some Smoky stuff:

http://mentalfloss.com/article/80484/13-fast-facts-about-smokey-and-bandit

I couldn't find a reference for your quote but it sounds so Smoky.

 

[OmCheeto]

Wow.I got interested,what exactly is that?

It's something I made up, because the "oh-plus" function was confusing me. (Still is actually. As I said, it's going to take me a while to learn this.)

\begin{matrix}
x & & y & & x⊕y\\
o∆8 & * & o∆8 & = & o∆8\\
\\
diamond & of & doom?\\
x & & y & & x⊕y\\
o◊8 & * & o◊8 & = & o◊8\\
1/x & & 1/y & & 1/(1/x+1/y)
\end{matrix}

I think it might come in handy when first introducing the concept. It strikes me as kind of heuristic. And then as the student become familiar with the process, it morphs into the triangle.
Much like when introducing multiplication:
4 times 5 is equal to 5 + 5 + 5 + 5
which eventually morphs into
4 x 5

It becomes a "generally" understood shorthand concept.

And the diamond actually contains both the symbols for exponentiation(^) and root(√), which the 2nd grade teacher can doodle in full color. Mostly in preparation for students going on, and interacting with old teachers, who still stubbornly use the old symbols.

Btw, I researched the origins of the triangle the best I could, and found the original stackexchange thread:

2011.03.31 (7½ years ago)
https://math.stackexchange.com/questions/30046/alternative-notation-for-exponents-logs-and-roots​

Grant published his video 2⅓ years ago.

So it should probably give the old timers some solace, that only two people have looked into it after 7½ years.
(Guessing you and I make it 4 now. Though I'm not sure I'm going to like it when I get done. But I'm pretty sure I'll have learned a lot of interesting things on my way there.)

 

[OmCheeto]

But I'm pretty sure I'll have learned a lot of interesting things on my way there.

Because of this thread, somewhere in the last 12 hours, I found out that exponential and polynomial growth are two different things.*

And before anyone yells at me, I had someone on on the internets ask me the other day if I was being purposely obtuse.
I told them quite honestly; "No, I really am this stupid".

------------
*Well, they both have exponents, so they must be the same thing.
Yay learning!

 

[jedishrfu]

Is it acute obtuseness or equilaterally spread out?

 

[jedishrfu]

Now back to our regularly scheduled thread already in progress...

@Young physicist perhaps you could develop an educational game from the notation to play with your classmates. If its clever enough it might even go viral. One strategy would be colpex triangle expressions on a card and the goal is the first to reduce it correctly.

I am reminded of the the Wff N Proof games of the 1960's where you used specially constructed dice to form valid logical expressions and then tried to prove them. We had a lot of fun playing it after school until the principal came by and told us it was illegal to gamble in school. We showed him it wasn't gambling but his authoritarian instinct told him that if it looks like gambling and smells like gambling then other students will do the same and the whole school will break out with gambling logicitis.

A wff is a well-formed formula. Now of course schools are more enlightened (actually the student of yore are the teachers today -- generational acceptance) and some encourage game play.



http://americanhistory.si.edu/collections/search/object/nmah_694594

https://www.oercommons.org/authoring/1364-basic-wff-n-proof-a-teaching-guide/view#h1

 

[Mark44]

I think it time to close this thread

Yes, well past time.

Thread closed.