Level Math 1

2.828
2.828

**Survival Difficulty: Class \(2\sqrt{2}\)**
»⠀Unsafe
»⠀Secure
»⠀High Entity Count

## Description

* **Level Math 1** is the second level of Mathrooms.
* The appearance of this level is similar to Level 10.
* Wheat in this level is advised not to be touched by wanderers, as it has a high probability of angering the entity "Equation".
* The coordinates in this level seem to be distorted by the sine function, where the original coordinates \((x, y)\) become \(x + \sin x, y + \sin y\). (Using mathematical knowledge, it can be proven that this mapping is a bijective function from \(\mathbb R^2\) to \(\mathbb R^2\), so there is no need to worry about falling into the void where there are no original coordinates)
* There are moderate entities called "Equations" in this level.

## Entities

### The Equation

* The appearance and behavior of the Equation resemble that of a snake.
* It consists of equations in the form \(f(x)=b\), where \(f\) is an elementary function.
* The Equation is scored in the following ways:
	+ Find all \(x \in \mathbb R\) that satisfy the equation and express them all in analytical form - 4 points (e.g., \(\{\sqrt 2,-\sqrt 2\}\))
	+ Find all \(x \in \mathbb R\) that satisfy the equation and express at least one in numerical form - 3 points (e.g., \(\{\sqrt 2,-1.41421\dots\}\))
	+ Find at least one \(x \in \mathbb R\) that satisfies the equation and express all in analytical form - 2 points (e.g., \(\{\sqrt 2\}\))
	+ Find at least one \(x \in \mathbb R\) that satisfies the equation and express all in numerical form - 1 point (e.g., \(\{1.41421\dots\}\))
	+ Otherwise, 0 points
* All numerical solutions must have an absolute error sum or relative error not exceeding \(10^{-4}\).
* The Equation poses a certain level of danger, which is also represented on a scale of \([0, 4]\). The more complex the equation, the higher the danger value.
* Once you are within 5 meters of the Equation, you will be unable to move, and you have 20 minutes to solve the equation.
* When you present an answer to the Equation in any form, it will be instantly scored.
* Let \(x\) be the danger value of the Equation and \(y\) be your score. \(z = y - x\), then
	+ When \(z > 0\): Taming the Equation, it will assist wanderers in solving other equations. At this point, the Equation's ability to solve equations will be multiplied by \(\dfrac z2\).
	+ When \(z = 0\): The Equation will be friendly towards you but will not help in solving equations.
	+ When \(z = (-1)\): The Equation will lightly injure the wanderer but will not require them to solve equations again.
	+ When \(z = (-2)\): The Equation will severely injure the wanderer but will not require them to solve equations again.
	+ When \(z \leqslant (-3)\): The Equation will fatally strike the wanderer.
* When a wanderer touches the wheat field, there is a high probability that the danger value of their equation will increase by 1.
* The Equation has a variant: the unsolvable equation, in which case the answer "No solution" or \(\varnothing\) is sufficient.

 File:方程蛇.PNG
### "0"

"0" is a flying entity that **cannot be touched by any three-dimensional object**. It appears white and is friendly in this level.

## Locations and Outposts

### M.E.G.Math m-α Base

* Belongs to M.E.G.Math.
* Friendly and open to trade.
* Provides tamed "Equations".
* Approximately 70 people.

## Entrances and Exits

### Entrances

* Find a door in Level Math 0 and enter through it.
* Being caught by Entity Math 6 may lead to entering this level.

### Exits

* As mentioned above, find a black cloth (or black towel) and cover your head with it. Enter a rare maze, and upon removing the cloth, you will arrive at Level 6.
* Survive for 1 hour to reach Level Math 0~3.
* If buried by more than 6 "Equations" in this level, you will be transported to Level Math 1-i.

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