ruk·si

# 🧮 Mathematics

Updated at 2011-01-05 17:00

Mathematics is an abstraction. Instead of thinking about particular numbers, mathematics focuses on the underlying patterns.

This note contains basic math formulas and terms that I mix up on a semi-regular basis.

Math:

• Theorem: A pattern or rule.
• Proof: Calculations that show that a theorem is always true.

Circle:

• Center: Every point of a circle have the same distance from this point.
• Edge: Points that form the outline of a circle.
• Radius: Distance from the center to the edge.
• Circumference: Distance of the edge.
• Diameter: Distance from an edge point to opposite point. Twice the radius.
• Pi: Ratio between circumference and diameter. Always 3.141559...

Average (Arithmetic Mean): The sum of collection of values divided by the number of values in the collection.

``````sum(x) / x.length
``````

Mid-range: Average of the minimum and maximum values in a collection.

``````( max(x) + min(x) ) / 2
``````

Median: The middle value in an ordered collection of value. If there is a even number of numbers, median is average of the two middle numbers.

``````x = [a, b, c, d, e]
^     ^     ^
min.  med.  max.
``````

Mode: The most common value in a collection of values.

``````x[a, a, b, c, c, b, b] = Mode is b
``````

Quadratic is a generalization of conic sections such as ellipses, circles, parabolas and hyperbolas. Think of a 3D cone where you cut slices.

Transpose is flipping matrix rows to columns and columns to rows over its the diagonal, `A` vs `A^T`.

Ordinal data is a categorical data type where the variables have ordered categories and the distances between the categories are not known.