### Background

Last year, I made an iPhone using about 350 linear, conic, and piecewise functions. It took about 20 hours to make and was meant to model an iPhone home display. It is actually supposed to have animation, but due to the sheer number of equations, my browser would constantly crash if I tried it. I own a Mac with Retina display so I do not encourage you to try the animation.

This is one of my favorite projects and definitely the one that I take the most pride in. I spent loads more time on it than was probably healthy, but I just had a lot of fun with it.

Here is the link to the graph: https://www.desmos.com/calculator/b2qi05nasi

My graph was actually featured as one of the “Creative Picks” for the Desmos site! My graph was sent out on one of the monthy Desmos newsletters to the tens of thousands of Desmos users.

### Screenshots

Here is a screenshot of the final creation:

Here are the different types of equations I used and the total times I used them.

Below are images of the finsihed product with each function labeled. The number corresponds to the function on the Desmos file as well as the number on the list of all the functions.

Circles:
2, 3, 4, 5, 6, 16, 17, 18, 19, 31, 32, 33, 34, 43, 44, 56, 57, 58, 61, 68, 69, 88, 89, 90, 91, 92, 93, 98, 100, 115, 117, 125, 126, 127, 128, 141, 142, 150, 151, 152, 153, 154, 158, 159, 160, 161, 162, 163, 169, 170, 171, 172, 176, 177, 181, 182, 184, 189, 190, 194, 195, 199, 200, 204, 205, 220, 224, 225, 230, 231, 253, 254, 260, 273, 274, 281, 282, 283, 284, 291, 192, 298, 299, 306, 307, 308, 316, 317, 318, 324.

Ellipses:
7, 8, 27, 37, 38, 59, 62, 102, 103, 104, 105, 106, 107, 108, 109, 129, 133, 143, 185, 296, 310, 312.

Hyperbolas:
9, 10, 20, 22, 25, 26, 29, 30, 35, 36, 39, 41, 42, 45, 48, 51, 52, 54, 55, 60, 66, 67, 86, 87, 99, 101, 113, 114, 116, 121, 122, 139, 140, 156, 157, 165, 166, 167, 168, 174, 175, 179, 180, 187, 188, 197, 198, 202, 203, 222, 223, 251, 252, 258, 270, 271, 272, 286, 287, 289, 290, 304, 305, 314, 315.

Parabolas:
21, 23, 24, 70, 71, 72, 73, 96, 123, 134, 135, 267, 268, 275, 276, 277, 294, 302, 309.

Lines (Linear Equations):
11, 12, 13, 14, 49, 50, 63, 64, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 94, 95, 111, 112, 124, 130, 137, 144, 145, 146, 147, 148, 149, 183, 215, 232, 233, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 255, 256, 257, 259, 261, 263, 264, 265, 266, 278, 279, 285, 293, 295, 300, 301, 311, 319, 320, 321, 322, 325.

Semicircles:
46, 47, 120, 131, 132, 192, 193, 206, 207, 208, 209, 210, 211, 212, 213, 216, 217, 218, 219, 226, 227, 228, 229, 234.

Sine Wave (Trig Functions):
118, 119, 120.

Piecewise Function (Two Lines):
214.

Animation Slider:
1.

Place Holders:
15, 28, 40, 53, 65, 85, 97, 110, 138, 155, 164, 173, 178, 186, 191, 196, 201, 221, 250, 262, 269, 280, 288, 297, 303, 313, 323.

### Piston Animation (Also a Staff Pick)

I also created a piston animation graph that was featured as one of the “Favorite Graphs of the Month.” Here is the link: https://www.desmos.com/calculator/o6zbu8pofe

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