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Akano's Blog



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Thesis Submitted

Posted by Akano , in Life Apr 11 2017 · 97 views
Huzzah!
Six years, four papers, and 179 pages later, I have submitted my Ph.D. thesis.

Now I have to defend it. But first, STRESS RELIEF VIA VIDEO GAMES!


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Specter of Torment

Posted by Akano , in Life, Video Games Apr 08 2017 · 39 views
Torment intensifies and 3 more...

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Seriously, this game is awesome. I can't wait for it to come out on Wii U/3DS so I can play it with a for reals controller rather than a keyboard.

Also I submit my thesis on Monday. That's cool.

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My birthday was all right

Posted by Akano , in Life Mar 01 2017 · 80 views

So, a week ago was my birfday. Usually I make an entry, but last week I came down with a head cold that left me a little out of it. Thanks to everyone who replied to the birthday topic that Tekulo posted in the wrong forum; it was very kind. ^_^

Now I'm feeling much better (though my throat is still a little phlegm-y). I'm also SUPER stoked for the release of Shovel Knight: Specter of Torment, which cannot come out soon enough on non-Switch consoles. One of the developers called it the Majora's Mask to Shovel Knight's Ocarina of Time. *hype intensifies*





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That moment when you realize

Posted by Akano , in Life Feb 17 2017 · 127 views
Coincidence?!, Yes and 1 more...
...that your two blog entries on pentagrams are six days short of being exactly one year apart from one another.

lel

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Equation of the Day #19: Golden Pentagrams

Posted by Akano , in Math/Physics Feb 10 2017 · 162 views
Pentagram, Five, Golden Ratio and 2 more...

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Ah, the pentagram, a shape associated with a variety of different ideas, some holy, some less savory. But to me, it's a golden figure, and not just because of how I chose to render it here. The pentagram has a connection with the golden ratio, which is defined as

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This number is tied to the Fibonacci sequence and the Lucas numbers and seems to crop up a lot in nature (although how much it crops up is disputed). It turns out that the various line segments present in the pentagram are in golden ratio with one another.

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In the image above, the ratio of red:green = green:blue = blue:black is the golden ratio. The reason for this is not immediately obvious and requires a bit of digging, but the proof is fairly straightforward and boils down to a simple statement.

First, let's consider the pentagon at the center of the pentagram. What is the angle at each corner of a pentagon? There's a clever way to deduce this. It's not quite clear what the interior angle is (that is, the angle on the inside of the shape at an individual corner), but it's quite easy to get the exterior angle.


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The exterior angle of the pentagon (which is the angle of the base of the triangles that form the points of the pentagram) is equal to 1/5 of a complete revolution around the circle, or 72°. For the moment, let's call this angle 2θ. To get the angle that forms the points of the pentagram, we need to invoke the fact that the sum of all angles in a triangle must equal 180°. Thus, the angle at the top is 180° – 72° – 72° = 36°. This angle I will call θ. While I'm at it, I'm going to label the sides of the triangle x and s (the blue and black line segments from earlier, respectively).

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We're nearly there! We just have one more angle to determine, and that's the first angle I mentioned – the interior angle of the pentagon. Well, we know that the interior angle added to the exterior angle must be 180°, since the angles both lie on a straight line, so the interior angle is 180° – 72° = 108° = 3θ. Combining the pentagon and the triangle, we obtain the following picture.

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Now you can probably tell why I labeled the angles the way I did; they are all multiples of 36°. What we want to show is that the ratio x/s is the golden ratio. By invoking the Law of sines on the two isosceles triangles in the image above, we can show that

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This equation just simplifies to sin 2θ = sin 3θ. With some useful trigonometric identities, we get a quadratic equation which we can solve for cos θ.

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Solving this quadratic equation yields

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which, when taken together with the equation for x/s, shows that x/s is indeed the golden ratio! Huzzah!

The reason the pentagram and pentagon are so closely tied to the golden ratio has to do with the fact that the angles they contain are multiples of the same angle, 36°, or one-tenth of a full rotation of the circle. Additionally, since the regular dodecahedron (d12) and regular icosahedron (d20) contain pentagons, the golden ratio is abound in them as well.

As a fun bonus fact, the two isosceles triangles are known as the golden triangle (all acute angles) and the golden gnomon (obtuse triangle), and are the two unique isosceles triangles whose sides are in golden ratio with one another.

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So the next time you see the star on a Christmas tree, the rank of a military officer, or the geocentric orbit of Venus, think of the number that lurks within those five-pointed shapes.

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Shoveled Knight

Posted by Akano , in Video Games Jan 24 2017 · 130 views
Shovel Knight, The Enchantress and 3 more...

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I'm kinda in love with this game. Also the soundtrack. Virt can lay down some sick tracks, yo.

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Me playing Pokémon Moon

Posted by Akano , in Video Games, Life Dec 02 2016 · 191 views

Me: "Hau just handed me a person named Max Potion. I think that's human trafficking."

KK: *bursts into laughter*

Me: *joins in laughter because he didn't expect that joke to land*

Another typical Friday evening.

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I had Christmas down in Africa

Posted by Akano , Dec 01 2016 · 187 views
Five Golden Rings and 3 more...


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Nothing worth having comes without some kind of fight

Posted by Akano , in Life Nov 09 2016 · 147 views

You've gotta kick at the darkness 'til it bleeds daylight.



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Exercise those rights

Posted by Akano , in Life Nov 08 2016 · 198 views
Yes We Stan, Vote, Be heard
Go vote.

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Oak Log Bans

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About Me

Akano
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Premier Members
Stone Champion Nuva
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1,500+ posts
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Proto
+2 for Premier Membership
+1 from Pohuaki for reporting various things in Artwork


Name: Akano
Real Name: Forever Shrouded in Mystery :P
Age: 28
Gender: Male
Likes: Science, Math, LEGO, Bionicle, Comics, Yellow, Voice Acting, Pixel Art, Video Games
Notable Facts: One of the few Comic Veterans still around
Has been a LEGO fan since ~1996
Bionicle fan from the beginning
Twitter: @akanotoe

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My Lovely Topics

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Hieroglyphs And The Like

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