[Contest] Valentine's Day Celebration @ 2017

Image Courtesy: Dekh News

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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    # I indented these lines
    # 4 spaces, and now they show
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    print "hello world"

# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"

Math

Appears as

Remember to wrap math in $ ... $ or \[ ... \] to ensure proper formatting.

2 \times 3

2 \times 3

2^{34}

2^{34}

a_{i-1}

a_{i-1}

\frac{2}{3}

\frac{2}{3}

\sqrt{2}

\sqrt{2}

\sum_{i=1}^3

\sum_{i=1}^3

\sin \theta

\sin \theta

\boxed{123}

\boxed{123}

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

I'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

Julian Poon - 4 years, 4 months ago

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

Michael Huang - 4 years, 4 months ago

2) This is swoon illustrated.

Michael Mendrin - 4 years, 4 months ago

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.

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

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

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

The Strange and Secret Notes of Lovers

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 chapter begins here: Me Want a Heart Limb!

Please keep track of all the submissions. indicated by bolded texts!

Second chapter: Valentine Pool

Summary: 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!

Wow, you have nifty geometry skills

Agnishom Chattopadhyay - 4 years, 4 months ago

@Agnishom Chattopadhyay – Fixed the answer and the details for the second submission. Sorry for changing the links so quickly without double-checking!

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 :)

Here is the interesting Reuleaux Rose I created via Geogebra:

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

@Michael Huang – Fourth chapter: Reuleaux Rosie

It's now Yugi and Tea's turn! :)

@Michael Huang – 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.

@Michael Huang – Fifth chapter submission: Hearty Pattern

Hehe. 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

@Michael Huang – Michael, you're going to win this contest, you know that don't you? At least for making it the most entertaining.

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$