Summer of Math Exposition

Presented by 3Blue1Brown 3blue1brown

Visual intuition for exponential growth

Audience:

Tags: algebra-iiexponential-growthpolynomial-growth

Shows why 2^x grows faster than x^2, using bananagrams tiles to show a visual intuition. For high school students learning about exponential functions, or a general audience curious for new perspectives on simple math, or even a more advanced audience interested in new perspectives.


Analytics

6.87 Overall score*
32 Rank
15 Votes
10 Comments

Comments

4.9

completing the explanation

6.8

I liked this video a lot because it was engaging from the get go. This exposition was short and sweet and builds fundamentals of understanding how to think about growth of functions students will see IRL for the long-term— plot some points, and map it. That being said, I’ve got some feedback for the “Clarity” criteria. At 3:22 you took 2^2=4 and added that next layer to get 3^2= and said, “…add this row here… just like an onion.” But I think you need to reevalute the choice of words, because these weren’t only rows, they were rows and columns, and the analogy of onion would be more understood if you used the word “layering.” It is implicitly understood the tiles were being layered. Finally, I’m a little hesitant on accepting this intuition that we only need to remember the outer layer because with math we intuitively evaluate each unit to build a whole. So perhaps instead of saying we only need to pay attention to the outer layer, we can pay attention that the squares are added by each consecutive odd integer to make the square (e.g for 9=1+3+5, and you can see this on the bananagram tiles as you add each layer, you use its successive odd integer. So, this also proves that we are considering the whole square and its individual parts. But overall, keep making more videos because they’re engaging! These were your individual scores per each criteria that contributed to your overall Ranking score: Motivation: 9 Clarity: 2 Novelty: 7 Memorability: 9

7.2

You did an incredible job at explaining it very simple and clear, so there was nothing confusing about it.

6.9

Very interesting question explained clearly and visually. Excellent! 👍

3.4

Lengthy presentation of a simple topic. The idea of using tiles as support is good; perhaps it would have been more interesting to see it applied to more complex topics for the students.

6.4

Short but concise video explaining exponential function. Good piece

4

its a great math video but would be better with a better visual

8

Loved this! What a great approach, using both numerics and visuals.

6.9

Showing the unlabeled graphs at the beginning really solidified the motivation. The use of tiles to represent relevant multiplications was intuitive.

5

Excellent Concept. Visual presentation could have been more graphic.