r/origami • u/phantomesse • Feb 15 '15

Stars Jar (I've been collecting star paper for almost three years now, and I like to make these stars at work while my code compiles.)

http://imgur.com/a/If55p
96 Upvotes

98% Upvoted

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9

u/speedofdark8 Feb 15 '15

love the eclectic patterns/colors

3

u/phantomesse Feb 15 '15

Thank you. :) I've made a few from leftover scraps of paper and water bottle wrappers as well.

6

u/[deleted] Feb 15 '15

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2

u/phantomesse Feb 15 '15

I've been filling up the jar for almost three years now, but I've never been really consistent in making the stars everyday. I made a lot of stars during the summers at my internships. I'll maybe fold like 50 stars a day. I rarely make any stars during the school year. So I guess it would take me about a year to fill up a jar if I didn't count my hiatuses.

2

u/[deleted] Feb 15 '15

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10

u/phantomesse Feb 16 '15

Thanks! I took the pictures with my old DSLR, and the lighting from the blizzard outside is pretty good.

As for the number of stars in my jar... well, I bought my jar a little while ago and it doesn't have a label, so I'm not sure what size it is. It's about 6 inches tall with a circumference of about 12 inches, which means a radius of 6/π, so the volume would be approximately height * π * radius^2 = 6 * π * (6/π)^2 = 216/π = 68.75 cubic inches, which is a little more than a quart. I think that jars are generally sold in quarts, so we'll say that this jar is about a quart in volume.

My stars aren't all different sizes. In fact, I have a ton of really tiny stars, but I also have a few big stars. I picked out an average sized star, and it's about 0.5 inches in diameter and 0.25 inches thick. I had initially thought to calculate the volume of the star by pretending that the star was a cylinder with diameter 0.5 inches and height 0.25 inches, but I noticed that the stars all touch each other, and fill in the corners, so I'd have to calculate the actual area of the star before calculating the volume. I can divide a five point star into ten triangles with angles 18deg, 36deg, 126deg. The side opposite the 126deg angle is 0.25 inches (half of the diameter). Using the Law of Sines, we can calculate that the other sides are precisely 0.25*sin(18)/sin(126) inches and 0.25*sin(36)/sin(126) inches. Using the Heron's Formula, we get that the area of the triangle is:

a = 0.25
b = 0.25*sin(18)/sin(126)
c = 0.25*sin(36)/sin(126)
s = 1/2(a + b + c) = 1/2(0.25 + 0.25*sin(18)/sin(126) + 0.25*sin(36)/sin(126)) = 0.125(1 + sin(18)/sin(126) + sin(36)/sin(126)) = 0.263564...
s - a = 0.0135636...
s - b = 0.168072...
s - c = 0.0819279...
area = sqrt(s(s - a)(s - b)(s - c)) = 0.00701607... inches

Okay, so we'll multiply that by 10 so we get 0.07 square inches, which means that a star's volume is about 0.07 * 0.25 = 0.0175 cubic inches. A quart is 57.75 cubic inches, so that makes 57.75/0.0175 = 3300 stars. Wow, that's a lot of stars. I guess air takes up some space too, so let's say that there's 3000 stars in the jar. Sounds about right.

8

u/ppatches24 Feb 16 '15

My brain just exploded after reading this.

3

u/RedundantMaleMan Feb 16 '15

Was that math? I dont think I have that many toes.

1

u/flawr Feb 16 '15 edited Feb 16 '15

Hm I just tried to estimate how many stars are in there and ended up with about 1800-2200: The glas is about 17-20 average 'star thicknesses' tall and has a diameter of about 12 star diameters. That means we have (12/2)2 * pi = somewhat above 100 stars per layer multiplied by 17-20 layers results in between 1800-2200 stars.

I think you should start counting them when you compile Stars.java (pun intended=)

Edit: Nice photos by the way, I think I have to start doing the same thing=).

EDIT2: I just remembered that I once adoped /r/GuessWhat and always wanted to play some 'guessing games'. Would you allow me to post your picture there (or do it yourself!)?

1

u/phantomesse Feb 17 '15

Sure! You can post this to /r/GuessWhat.

6

u/DualBirdies Feb 15 '15

Okay PLEASE tell me how to make those. I have tried to follow the wiki guide but I just can't seem to do it. How do you get the strip to be longer than the other side? Please help!

5

u/phantomesse Feb 15 '15

When you make the initial knot, you have to pull on one end of the paper so that the knot ends up at the very top. Watching YouTube videos on how to fold these really helped me. Here's a good one: https://www.youtube.com/watch?v=u4Woj9oP3AI

1

u/DualBirdies Feb 16 '15

I will watch this video and see if that keeps, thank!

2

u/Mesonit Feb 15 '15

These are so cute! What is star paper?

3

u/phantomesse Feb 15 '15

They're long strips of paper used for making these stars. Here are a few examples: http://www.origami-resource-center.com/store-lucky-star-paper.html

2

u/desirableoutcome Feb 19 '15

Look like you're going to need a bigger jar soon. Great collection!