Pool, otherwise known as pocket billiards in North America, is the family of cue sports played on a pool table. The pool (or billiards) table is typically rectangular and has six "pockets" along its sides. However, the key word here is "typically." For this project, we'll be making an elliptical pool table, basically, one in the shape of an ellipse.

An ellipse is a regular oval shape, traced by a point moving on a plane so that the sum of its distances from two other points (the foci) is constant. In Euclidean geometry, an ellipse is usually defined as the bounded case of a conic section, or as the set of points such that the sum of the distances to two fixed points (the foci) is constant.

Due to an the properties of an ellipse, at any given angle from one focal point will lead to the other. With this, we can make sure we always pocket the billiard (given the right conditions). The following video by Numberphiles demonstrates this perfectly, and is the inspiration for this project.

Sources: http://www.mathopenref.com/ellipsefoci.html (for some testing)
http://www.wikihow.com/Draw-an-Accurate-Ellipse (to confirm how to draw an ellipse)
http://www.purplemath.com/modules/ellipse.htm (basic info on ellipses)

Step 1: Collecting the Necessary Materials

First and foremost, you need to collect the necessary tools and materials. Most of these materials can be bought from the local hardware store, aside from the place you wish to work at. Some of them can even be interchangeable. You can make the ellipse however big you want. However, it'd be advisable to make sure the major axis and minor axis are relatively close in length, in order to prevent the focal points from getting too close to the walls. The project is pretty clear-cut. Heavy machinery will be used and precise measurements will be made, so please keep yourself safe and make sure to measure twice - and cut once. Sharpen your pencils and put on some safety glasses.

What You Need (for my version):

To Make the Pool Table:
- At least 1600 sq. inches of wood, preferably a hard, heavy type, at least 1.5" thick.
[In my case, I used medium density fiberboard, or MDF (the type used for office desks and chairs) which my school was itching to get rid of.]

- A 124" long piece of wood siding, foam, rubber, etc
- 124" of vinyl wall base molding (for aesthetic purposes)
- A box of nails (17-Gauge 3/4" Stainless Steel Wire Nails)
- Screws (2")
- String and a pencil
- Tools & heavy machinery (table saws, disc sanders, etc) to drill, cut, or make holes in the wood.
- And naturally, a cue stick and some billiard balls to play with
- Time and a couple people to help out

Approximate Cost of Project: (Excludes pre-bought tools and machinery)

The list of materials and resources to do this project is not very long, nor are any of the materials hard to get (save for the workplace). Being the frivolous person that I am, I mostly cannibalized and salvaged pieces in order to build my pool table. The only thing I actually needed to pay for was a box of screws and of course the time and effort put into the project. However, you may not actually have all these materials at your disposal. The pricing of materials needed here depend on your area and from where you buy them. The following prices are merely estimations to help you.
$10 worth of MDF panels, which were originally 2x (4'x2') pieces that were combined together
~ $4 of screws, nails, string
$14 of vinyl wall base molding (about 1.15 per foot)
$11.04 for 2x pool noodles
$13.56 cue sticks (nothing fancy)
$5.67 cue ball (or $24.95 for a full set of billiard balls)

Total: ~58.27, excluding electricity bill, tools and machinery, labor, and time.

*note - this is only the price of my pool table, and yours may different based on how big or small you make your ellipse. Certain materials might be changed. For example, instead of using noodles, I had some foam packaging that fit the same purpose, so I used those instead. Another note is that if you plan to make your elliptical pool table freestanding, it would be advised that you make some sort bag or cup to serve as the "pocket." My table simply rests on a flat surface and does not need a pocket. The table or surface underneath serves as the bottom.

Step 2: Drawing the Ellipse

After gathering the proper materials, the first logical step would be to draw the ellipse. After watching the video on elliptical pool tables, I became intrigued and wanted to get one myself. However, elliptical pool tables are hand made, and most are in the 4-digits regarding price. So unfortunately, my high school level job would not be helping me pay for that. The next logical step (at least for me) was to build one. Obviously. My trigonometry classes helped a lot regarding how to do this. Feel free to brush up on your knowledge about ellipses at http://www.purplemath.com/modules/ellipse.htm

In my situation, our high school had some extra particle board that they were probably never going to use, so I decided to use that for my project. However, they were pretty small pieces so I had to combine two of them together. If you have a large enough piece, carry on.

First off, find the dimensions of your wood. My piece of (combined) wood was exactly 38" by 40". With 40" being the longest side, 20.5" would be the length of the major axis, and 19" would be the minor axis. Next, find the center of the piece of wood. Mark it. Then, following standard procedure and using the correct formulas and equations (as shown in the picture), find the distance from the center to the foci. Mark those two points as well.

After finding the foci, hammer in a nail into each of them. Cut and tie a loop of string approximately twice the length of the major axis. Place the string circle over and pull tight against the two foci nails (as shown above in the second image) with a pencil. As you move the pencil from side to side, you will notice that the path of the points is curved, for lack of better words. If you keep going counter clockwise or clockwise, you will be able to draw an ellipse. Keep drawing the ellipse until you are satisfied with the shape. This can all be done due to the properties of an ellipse and its foci. Unlike a circle where the circumference is equidistant from the center at all points, the radii of ellipses fluctuate based on their position.

Step 3: Cutting Out the Ellipse

This step is the most time consuming and what I believe to be the hardest part of the project. After tracing the shape of the ellipse I wanted to cut out, I had to figure out HOW to cut it out. What you will need is a jigsaw, a handheld circular saw and a sander.

Using the circular saw, carefully make some relief cuts to the edge of the ellipse (as shown in images 1 and 2). Cut as much excess wood away from the edges to make it easier when cutting out the curved edge. Next, use the jigsaw to cut as close as possible to the lines on your table. Afterwards, use a sander to clean up the edges and remove anything jutting out from the sides. The finished product should look like image 3.

Next, you'll want to cut out your pocket for the table. We'll only need one. Remove the nails from your foci and use a power drill to predrill into one of them. Then, switch to a hole saw bit. Use this to make the hole for your pocket. The standard billiard ball's diameter is 5.715 cm, or 2.25", so make sure to use a bit that is a little bigger than that, but not by too much.

All of this is easier said than done.

Step 4: Bumpers and Rails

The last step is to add the rails and bumpers of the pool table. Simply find a suitable piece of foam, wood, rubber etc to use, and screw it down or onto the table along its edges. I added some vinyl wall base molding for the sake of aesthetics and to cover up any gaps between the bumper and the table.

Step 5: Test It Out

Now all you have to do is simply test it out for yourself! As stated before, as long as you hit the ball with the right amount of force and from a focal point, it should rebound to the other focal point, no matter which angle you hit it from.

Step 6: Time and Effort Analysis

The total time required to build the pool table was approximately 8-9 hours spread out over a period of time. I built it over a time span of about two weeks, working on it an hour or so every other day. If done continuously without stopping one could easily complete it within a day.

Time spent on the project on different parts was miscellaneous, including but not limited to cutting the ellipse, designing parts, and trying different things with trial and error.

Step 7: Improvements

If I had the time to redo the project, there would be a couple things I'd like to try. For one, I'd like to make the pool table bigger, maybe add some green felt for a more authentic look, and put actual rails and bumpers onto it. I feel as if this would make the project 5x better, if only I had the time and resources to do so. I'd also like to attempt to make the table a stand alone, and create an actual pocket for the table.