Shapes of Numbers
Numbers are perhaps the oldest language known to humanity. It has persisted in one form over the course of history and understanding them allows both understanding of natural and social processes perhaps even of more sublime forces This note is to collect figures and definitions to help me gain a better understanding of mathematics in general.
- Ratio
- A relation indicating how many times one number contains another number. (eg. "The ratio of Mass to Velocity is Force" is the same as "Force is how much velocity a certain mass contains")
- Represents an inverse relationship, where an increase in one term is a decrease in another term, vice versa.
- Product
- A relation in which two values multiply each other, the inverse of a ratio.
- Represents a direct relationship, where the increase in one term also means an increase in the other.
- Scale
- Scalar Quantity
- A pure abstract value, used to measure the magnitude of a term.
- Is usually the component of a given vector.
- Line Segment
- Distance between two points in a given coordinate space
- Vector
- Vector Quantity
- A value representing a term with both magnitude and direction.
- Is a line segment where one line is designated as origin and the other as direction.
- Is composed of scalar values in an n-dimensional Cartesian plane. eg. A vector in 2d space is (x, y), a 3d vector being (x, y, z), and so on
- The magnitude of the vector is represented by its length.
- Scalar components of a vector represent distance from a given zero-point origin. eg. A vector ,(code [O->A]) where Origin `O` is (0, 0) and Point `A` is (2, 3), it is unnessary to include the zero-point origin, making the above example equivalent to just ,(code [->A]).
- Vectors of similar direction and magnitude are equal.
- Polynomials
- Algebraic expressions consisting of variables and coefficients.
- Variables
- sometimes called indeterminates, these are quantities that may change depending on the context of the equation.
- Coefficient
- The value to which terms are multiplied to.