I've made an introduction post for myself, but I wanted to make an official post under this category for my completed game, squareroot2.

Basically for all of this I have been the Red Mage of game creators.

Link: squareroot2 on Google Play

The link contains gameplay video and screenshots.

Personal reviews so far have been that it's pretty hard.

This game is is only a 30MB download, and runs an average of 14MB memory usage. This is without further optimizations. Sprites are relatively around the range of 512x512, even if some look incredibly small on screen.

Game Dev Stats:

build start to launch: 1.5 months

Unity Game Engine - (using MonoDevelop and C#)

MediaBang Paint Pro for Sprites. This program is traditionally made for Manga and Comic artists.

as3sfxr for Sound Effects.

Java using Apfloat Library to build a 141421 size string carrying that many digits of √2 (1.41421536... to infinity). The inspiration for this game. This digit is encoded in all sorts of different ways in the physics and timing of the game. The digits are also created on every platform, beginning with 1.414.. which resets on every start. Thus encoding the digit into the game design. Hence the character's name, squareroot2, is a square and lives in a squareish world.

Branding and Logo:

I want to make fun games for Everyone.

zareth_ElementZ

zareth = The very first character I came up with. I have had this name with me since 7th grade.

ElementZ = My love for Numbers and the concept of "Circling the Square" or what some believe as "Doing the Impossible!" (look it up, it's fascinating.)

tldr version: A single infinitely small number and a single infinitely big number make it possible.

//alert Numbers nerd Design stuff //

Circling the square creates the number Zi, an irrational number, 1.2732395447351626861510701069801... which is the ratio of a square that surrounds a circle with the circumference of 1. The assertion is made in that a circle can be assumed in the means of powers of 2 ( 2^{^}n) in the same exact way we describe a square, in which case the transcendence of the number becomes embued in the surrounding square (Zi). This is as opposed to our assumption of a square being whole digits and then transcending to the number Pi to describe a circle.

In which case there are two transcendent geometric languages: Pi (3.1415...), and Zi (1.27239...).

My proof is in the algorithm I created, that begins (assumes) the √2 to calculate Pi (if we can assume infinitely all digits of √2, then all those digits can assume every digit infinitely of Pi). This is a geometrical calculation, much like ancient Greeks performed their math. I divide a circle of the circumference of 1 by 2 continuously, (0.5, 0.25, 0.125...). It calculates an Infinitesimal. The number I've called "s". This is a value that calculates both Pi and Zi.

It can be found using Zareth's method (my formula, using https://keisan.casio.com/calculator):

/* Table and chart of the Zareth method */

s = (sqrt(.5));

c = sqrt(2);

for (y = 1; y < x; y= y + 1)

{

s = (sqrt(((c/2-1)^2) + (s^2)))/2;

c = sqrt(2 + c);

}

s;

Output:

x s

0 1.414213562373095048802

1 0.7071067811865475244008

2 0.3826834323650897717285

3 0.1950903220161282678483

4 0.0980171403295606019942

5 0.04906767432741801425496

6 0.02454122852291228803174

7 0.01227153828571992607941

8 0.00613588464915447535964

9 0.003067956762965976270145

10 0.001533980186284765612304

This Number, s, corresponds to each division of a circle by 2. Creating a polygon (squares) of 2^{^}n sides, (2, 4, 8, 16, 32........ 512, 1024, and so on, which can grow infinitely).

Therefore these values of s can also be assumed to be values of 1 / 2 infinitely (1, 0.5, 0.25...)

In which case both exist simultaneously as the same number at a sufficiently low decimal point, given the precision needed for the calculation. And therefore a polygon of sufficiently high side count is indistinguishable from any circle.

Using the values of s (above), I created the circles and other shapes to create ElementZ (assuming a polygon of 2^n). Pi is not used in the calculates at all.

ElementZ is then created strictly by code in this structure, using only the LineRenderer in Unity, creating an awesome partner with Zareth.