Learning math? Think like a cartoonist


This is a companion discussion topic for the original entry at http://betterexplained.com/articles/math-cartoonist/

Thanks Dora, that’s a great idea. Trying to visualize ideas on your own is a good way to come up with new explanations, and one of your students might have a neat cartoon that helps the whole class!

@Roberto, thanks for the pointer! I’ve just gotten in touch with Prof. Oakley, who is running the course ;).

@abhisek: I’d like to cover this topic too, thanks for the suggestion!

@Yash, I have an article on the dot product here: http://betterexplained.com/articles/vector-calculus-understanding-the-dot-product/

I don’t have one on the cross product yet, but would like to cover it down the line.

Hi Tim! I totally agree - the practical essence of Euler’s formula can be taught early on. Later, we can dive into the details (if needed).

Your articles are excellent! So useful for me as a maths teacher in Italy. I want my students to create cartoons on any concept I teach them - I’m sure it will help them remember as well as making it fun!

Thanks for this post!
I visit the site every once in a while during the year and find something interesting always; you seem to have a gift for teaching. :slight_smile:

By the way, this is a little out-of-topic, but there’s a interesting course on Coursera called: “Learning How to Learn: Powerful mental tools to help you master tough subjects”, that started recently and seems to promote similar ideas to learn/understand more effectively complex topics, amongst other things.

Khalid, could you better explain to me the concept of “i” being a 90 degree rotation? I would be really interested. I just love connections and concepts

Definitely. Try checking out the article here, there’s some diagrams and a video as well:


In a nutshell, if we consider positive numbers to be forward, negative numbers to be backward, then imaginary numbers are sideways.

The main idea for imaginary numbers is that we don’t need to be stuck on the number line, we can take our numbers into 2d :).

Enjoy your articles--------> keep them coming! Thanks.

Thanks Jeffrey, I appreciate it.

What’s funny is that all of these concepts are available in high school, where Euler should be taught in freshman year.

Always a treat to see your insights !

Kalid, you’re the best!
Has someone ever asked you for permission to translate your articles to Portuguese? Sometimes I think about it. Could I do it with all the references? Actually, all your site, your book and your course deserve a full translation.

Kalid, please keep doing what you do, it’s amazing.

Neat summary!

@Pierre: Thank you!

@Frederico: Thank you! Yes, feel free to translate any articles you like and send me the link (or the text, and I can post them here). I’m keeping a list here: http://betterexplained.com/translations/

@John: Appreciate the encouragement, hope to keep going for a long, long time.

@Steve: Thanks!

Awesome. Are the Drawings yours?

@Mark: No, but I wish! They are from the blog post linked: http://www.tomrichmond.com/blog/2008/02/14/how-to-draw-caricatures-1-the-5-shapes/

Thanks for sharing this! We love the content and hope to keep seeing more great posts!

Wonderful as usual. I try to get students to think of written math as pictograms, like Chinese writing. Sadly, I don’t reach everyone with this analogy but those that get it seem to love it.