Think outside the box!

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What's the area of a single triangle?

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Book ratings are from January 2023.

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Mind Your Decisions: Five Book Compilation
A collection of 5 books:
"The Joy of Game Theory" rated 4.3/5 stars on 290 reviews
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews
"The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews
"Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews

Mind Your Puzzles: Collection Of Volumes 1 To 3
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 112 reviews
"Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews
"Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

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High School student: *solves it the uni way*

Docked points for not following instructions

misterchubbikins

more like think INSIDE the box

i will now see myself out(of the box)

alegitnolife

I have a way to connect the two methods: The triangle area is simply 1/2 a (a+1) or can also be written as 1/2 of (a^2 + a) so I decided to take 2a^2 + 2a +1 = 9 and subtract both sides by 1. Then just divide both sides by 4 to get the exact algebraic expression for the area of one triangle. It sorta algebraically fleshes out the visual argument on the university side by applying an expression to represent the triangle area.

UberHummus

It took me embarrassingly long to figure out where b= a+1 comes from. I think I need more sleep.

madcow

One of the few channels that try to make maths interesting to us. Thanks for making maths more accessible.

BrainPermaDeD

seriously, I solved it in my head. (not lying)
a² + b² = 9
let this equation be 1
b = a + 1
b - a = 1
square both sides
a² + b² - 2ab = 1
a² + b² = 1 + 2ab
let this equation be 2nd
subtract 2nd from 1st.
0 = 9 - (1+2ab)
0 = 8 - 2ab
2ab = 8
multiply by 1/4 on both sides
ab/2 = 2

syther

High School: *Albert Einstein Level*
University: *Elementary School Level*

이규헌-sc

the latter way is how primary students solve olympaid questions

fsyi

I paused at the start and was JUST starting to do things the "High School" method when my whole brain just went "WAIT A MINUTE" and realized the other way to do it.

WillRennar

Bro. Y'all are way over thinking this one. In the highschool method stop right there at a^2+a=4 because that's literally twice the area of that triangle.
a(a+1)=a^2+a=4. So, a(a+1)/2=2. Voila.

Math_Rap_and_GOP_Politics

by doing the university method, you concurrently assume that length 1 is exactly equal to length A

MacKo-ghoe

...If only the figures are to scale and you are free to slide'em on a sheet of paper while at the same time use them as proofs

-tg

This is really what I need, please make more of this videos👌😍🤯😘

Kshitij.with.nature-channel

How can we know these triangles are the same

luckypegasusvol

High school teachers: high school
Middle school students: university

MMiketro

University: teaches you to think simple
High school: teaches you to overthink.

mach

You should have wrote: "Think inside the box"

calholli

i dont get the university method, why can you just say the bottom part of the triangle has a length of one?

thebushmaster

Ph.D.: slides the triangles one unit outward in his head and concludes that he’s left with an outer square of area 9 minus a hole of area 1.

michaelz

In the final calculation on the HS side, should that 1 be squared?

dansouth

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