Bogus Mathematical Theorems
From Homestar Runner Wiki
Strong Bad periodically invents bogus mathematical theorems to illustrate his responses to fans on his Strong Bad Email show. Another was introduced to players of the third episode of Strong Bad's Cool Game For Attractive People. Two more were also added in the game Poker Night at the Inventory.
 The Transitive Butt Property
When the sender of email butt IQ is skeptical that any sort of IQ test exists to determine whether or not someone's butt is stupid, Strong Bad quickly refutes his ignorance with the following property:
Symbolically, this can be written as
 The Property of Ones
When a fan asks Strong Bad if he's ever had a one that was not cold, he responds by stating the Property of Ones: "The ONEitude is directly proportional to the Colditude of the ONE." Here follows a brief analysis of this statement.
We consider a One with the following properties:
- is a measure of the Oneness of the One.
- is the temperature of the One.
- is the coldness of the One.
The Oneness of the One can be determined by the following simple formula:
Naturally, a One has less coldness as its temperature increases, and it approaches having no coldness at all as its temperature approaches infinity. Likewise, a One approaches having infinite coldness as its temperature approaches absolute zero:
Thus, a One's coldness is inversely related to its temperature:
As a result, we can rewrite our expression for Oneness in terms of temperature:
so that is a proportionality constant (in units of Oneness times kelvins) that uniquely determines the Oneitude of a One given its temperature. If a One is not so cold, the temperature will be higher, thus minimizing its Oneness. In Strong Bad's own words, this can be simply stated:
The inverse is also true:
How large the proportional relation and what units are used for coldness and Oneness are undefined.
 Coolguy's Law
In order to assist an email sender who was having difficulty determining which slumber parties are worth attending, Strong Bad stated an important relation between the popularity of a potential party host and the amount of fun available to be had:
This law is illustrated symbolically by the following equation:
This means that the less popular the host is (in a numeric form), the more fun (again in numeric form) you can have at their house. How the numbers are determined is unclear.
 The Cooldratic Formula
Introduced in Baddest of the Bands, the entirety of the Cooldratic Formula is this:
Not surprisingly, Strong Bad introduced this formula shortly after pouring butter into a fog machine full of dry ice. He also briefly acknowledges the status of his formulas as bogus by stating "I'm no mathematician".
 Poker Night at the Inventory
Two minor theorems were included in Poker Night at the Inventory, but without any equations or mathematical proofs to them.
 The Reflexive Property
Introduced in Poker Night at the Inventory Strong Bad may say sometimes to Max and the Player when calling a bet: "I don't like either of you, but maybe calling you will cancel that out. You know, the Reflexive Property."
 The Inverse Property of Luck-Have
Also from Poker Night, upon the Player winning, Strong Bad may say: "Yeah, you're lucky now, but you know you're gonna get run over by a truck when you leave here. It's the Inverse Property of Luck-Have."