Summer of Math Exposition

The Cornu Spiral

An exploration of a fascinating curve called the Cornu spiral, and a new approximation for the coordinates of the curve.

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5 Overall score*
30 Votes
14 Comments
Rank 27

Comments

beautiful

9

This is way too short :( Please say a bit more about the actual application of the spiral (to make it more motivating - otherwise people not in the know might not understand why the Fresnel integral is important or why care about it), and tell me how you came up with the approximations in the first place.

5

It is too short, just a single sentence is not a proper 'Exposition'

1.1

Cool. It could have more interaction/animations. It could have more explanation, for example "tanh", "sech", I don't think I knew what those functions were when I had just don a trig class to be honest :)

5.1

Concise and pretty - but maybe a little too concise! It might’ve helped to see how exactly you derived these approximations, or where the cornu spiral comes from? Maybe some more historical perspective

6.1

Perhaps you could start with some motivations for why it's important? I thought it was beautiful, but it would have been great to see the applications at the beginning (instead of the end).

4

The article has nice visuals, but the content is very short. Needs more contribution.

5.6

This is the third attempt at feedback... Something's not right

6.2

Nice, clear explanation, with good visualizations. But I feel it's lacking in motivation, and consequently also memorability: other than one sentence in the conclusion, it doesn't really give me any reasons to care about the Cornu spiral, or your approximation of it.

4.8

While interesting, the article did not offer any motivation to study the Cornu spiral. This resulted in it sounding very dry and unmotivated. It would also have been nice to see the actual code in Julia and an explanation for how the approximate forms of the Fresnel integrals were arrived at. On the whole, the article did not help with understanding/learning something new and felt like reading a summary.

2.8

The topic was new to me, and it looks intriguing. The presentation was clear and the layout fine. Only, I really missed a piece of information that gave me an "aha" moment, even just a note about how you got intrigued by this curve.

4.5

Though it is a very interesting object, and one I was not aware of, it would be nice to understand how it arose in the first place, or detail a bit more what the applications are, in short giving more context.

5.1

Highly novel and memorable, but could go a bit deeper on the explanation/exposition. You just right into the math when some context and motivation would help up front.

7

I think that this article could benefit from having a little more info to help keep everyone on the same page without feeling lost. Currently, the article assumes a lot of prior knowledge, which may not be present in all viewers minds, or may need a slight refresher. Aside from that, this was quite enjoyable.

6