It is February again, and Valentine's Day is knocking at the door! With love undoubtedly in the air during this part of the year, let the brilliant minds light up the colors of Brilliant and set the pace for the celebration of love with their intellectual, yet romantic content.

To enter, please submit a link to your problem/note/wiki in the comments. Add (at most) one image, if you feel like it.

The problem/note/wiki must be related to Physics, Chemistry, Mathematics, Economics, Biology or Computer Science in some way. Needless to say, it must also relate to the contest theme.

Wikis are not jokes. If you wish to submit a wiki, please do not compromise with the integrity of wiki articles.

We are looking for the best content, not authors. So, you may submit more than one content.

The score of a content will be determined by number of upvotes. Winning entries will be selected with a probability directly proportional to the score of the submission.

The contest ends on February 14, 2017.

Keep the comment sections clean and constructive.

For an inspiration, see what the Brilliant romantics did in 2015 and 2016 ❤

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## Comments

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TopNewestI've got 2 little nuggets:

1: Graphing this simple equation generates an infinite number of hearts

\[\cos \left(y+\frac{\cos ^{-1}\left(\cos \left(2x\right)\right)}{\pi }\right)\sin \left(x\right)\ge 1\]

2: A very crude cloth animation done on desmos

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2) This is swoon illustrated.

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The second one must be my favorite, even though I like both graphs! :)

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Hmm, how did I miss all this action with Valentine's Day submissions? Well, here's one I did Cheating With A Valentine's Cake I don't know if this entry qualifies. If not, maybe I'll try another.

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I remembered seeing that difficult problem in the feed! :)

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I think I'll come up with something more fresh. I think this problem has freezer burn.

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Okay, here's my entry for the 2017 Valentine's Day contest, a fresh one

The Strange and Secret Notes of Lovers

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My submissions will involve the story of Mai Valentine and Joey Wheeler, characters both inspired by Yu-Gi-Oh!. Thus, the name I gave the problem set is

\[\heartsuit\,\heartsuit\,\large{\text{MR. HUANG'S MAI VALENTINE STORY}}\,\heartsuit\,\heartsuit\]

Note: I don't solely base on difficulty of the problems for each chapter. The difficulty varies throughout the story.First chapterbegins here: Me Want a Heart Limb!Please keep track of all the submissions. indicated by bolded texts!

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Third chapter:Lovely Heart Curve!What is better than drawing a boring heart shape? I know, it's wave graph since the look is captivating! :D

This time, a fun calculus problem. Don't want to rely only on geometry :)

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Here is the interesting Reuleaux Rose I created via Geogebra:

I am going to use this for the next problem. Isn't it beautiful? :)

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Fourth chapter:Reuleaux RosieIt's now Yugi and Tea's turn! :)

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Animated Submission:Here is an interesting 2D geometric heart figure animated by Geogebra.The black points indicate the fixed centers of the circles, and the two pairs of points on the symmetric lines are treated as compass points, where the large circular arcs are tangent to the small circles at the orange points. The green point along the vertical dashed line is clearly the intersection point of two wide arcs.

Here are few figures you will notice during the transformation: (1) Two overlapping circles, (2) Cardioid and (3) Sharpened heart curve that is like the second question submission of mine for this contest.

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Fifth chapter submission:Hearty PatternHehe. Seems like I am running out of ideas for questions since the images are better than questions/problems in many ways! Guess I will stop the problem submission and continue inventing some fun math images. XD

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Second chapter: Valentine PoolSummary: After planning a cake, Joey and Mai decided to construct a swimming pool! It is interesting to know how to calculate the area of the special \(\heartsuit\)-shape!

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Wow, you have nifty geometry skills

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