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About Photography / Student Official Beta Tester Seth ShepherdMale/United States Recent Activity
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SethKat
Seth Shepherd
Artist | Student | Photography
United States
Rock Hill, South Carolina

Alright guys, so something really awesome I learned in my Mathematical Reasoning Class. Pi can equal to 4. Yes, this is mathematically accurate. Don't believe me? That's okay, I didn't believe my professor either at first. But it's true. I'll need to inform y'all on a little background information before I go into the details, but it basically boils down to calculate we look at numbers.

The numbers that people are generally used to working with are calculated in something that's called the Euclidean Norm. The name sounds intimidating, but it's really not. To begin with what the Euclidean Norm, which for shortness we'll call "2 Norm," think of two points on the xy-plane. One at (1,0) and the other at (0,1). Actually, write this down, it's easier to understand if you can look at it. Now, the shortest distance between these two points is obviously a straight line that connects them. If you draw this line, you'll see that a right triangle forms from the straight line and the x and y axes. You are able to find the length of the straight line that connects the two points using Pythagorean's Theorem, which is the square root of 2. So, that's all fine and good, but not a lot of people bother to memorize what the square root of two is, so it's not always that helpful.

Furthermore, you can't walk a perfectly straight line from one point to another. Like, if you needed to get from one corner of a city block to the opposite corner, you can't walk a diagonal straight line across the block to this other point because there's probably a building between you and this other point. So, if you've still got the two points I mentioned earlier in your mind, think about walking from the point (0,1) to (1,0). You'll need to imagine walking down the y-axis until you reach the origin, and then walk along the x-axis in the positive direction. So, instead of trying to walk through a building, you walk down the first street, and along the second intersecting street. Now, think about how far you've just walked. By doing this, you are calculating the distance between two points by this formula: d((x1, y1),(x2, y2)) =
| x2 - x1 | + | y2 - y1 |. This is mathematically mapping the distance between two opposing corners of a city block by walking down the streets. By calculating distance this way, you are no longer working with numbers in 2 Norm, you are in what's called the Taxicab/Manhattan Norm (1 Norm). It makes sense why. You drive up the street, turn a 90 degree corner and drive down a different street. You've just gotten from one corner of a block to another.

Now with this idea in mind, start thinking about the unit circle in 2 Norm, where √(x2+y2) = 1 and Pi = C2r; where C is the circumference of the circle, and r is the radius. Now in 1 Norm, the unit circle looks like this. Yup, it's a square, but it's still called the unit circle. You're supposed to be confused by this, but just go with it anyway. Remember that the unit circle isn't just a line on a graph. It's the infinitely many points on the graph that form the shape of a circle. In 1 Norm, each of these coordinate points will add up to the number 1; (x,y) -> x + y = 1. Remember the distance formula above?

Let's use this to find the points between (1,0) and (0,1).
| 0 - 1 | + | 1 - 0 | = 2. A square has 4 sides (in case you were unaware of this) so C = 8 and the radius is 1 (because it's a unit circle). Since Pi = C2r, in the Taxicab/Manhattan Norm, Pi = 82(1) = 4!

I realize this might be difficult to follow, so if you're still unsure that all this means, take a look at this PowerPoint. It was make by my awesome professor and it goes more into detail about how Pi is derived and how you can calculate it in different Norms. Thank for reading. I hope you enjoyed it.
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:iconfizzyfoxy:
FizzyFoxy Featured By Owner Oct 22, 2014  Student Digital Artist
thanks for the fav!
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FiguraArto Featured By Owner Oct 2, 2014
Thank you very much!
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nickalive Featured By Owner Sep 19, 2014  Professional General Artist
thanks for the fav
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Heartthrobaryan Featured By Owner Aug 30, 2014  Student Traditional Artist
Thanks a lot for faving my " Edward Elric " :iconsayhiplz: :iconsuperonionplz: !! You rock just like him :iconrockingonionplz: Your gallery is awesome..., Great pics :D
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s-kmp Featured By Owner Jul 7, 2014
:w00t: Thanks for the Fave on Poppy after the rain 01 :)
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RayfordSteele Featured By Owner May 24, 2014  Hobbyist Photographer
Dude Louie's "Fearless" sermon is like my favorite message EVER. I have it bookmarked and on my phone at all times haha 
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:iconskarzynscy:
skarzynscy Featured By Owner May 21, 2014
Hello Seth!
Hot thanks for adding my "The Edge - Cricoteka - Cracow" to Your fav.

In my gallery i have many others photos from interesting places (my Cracow, Praha, Mallorca, Mellorca, Morocco, Rodos, Sicily, Zakinthos, Florida) and beautiful flowers, trees, animals etc.
Maybe You find something...
Greetings from Poland!

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seek-and-hide Featured By Owner May 17, 2014  Hobbyist General Artist
Hello dear Seth,

Many thanks kindly. Your support is greatly appreciated. I wish you a wonderful week.

Mayumi
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CrystalCircle Featured By Owner Apr 7, 2014  Hobbyist Digital Artist
Thanks for the fave! ^^
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R3Create Featured By Owner Mar 22, 2014
HOW MANY TIMES WILL YOU CHANGE YOUR NAAAAME

I liked the original SethyKitty best :P
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