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Glossary

 

chunk (as a verb)

Put an expression or collection of symbols together in a group, so that something can be done mathematically with it.

chunk (as a noun)

An expression or collection of symbols that are put into a group, so that something can be done mathematically with it.

equation

A mathematical statement that two expressions are equal to each other. Generally, anything with an equals sign (=) in it.

expression

A collection of quantities, variables and operations. It evaluates to a number, if specific values are plugged in for the variables. 2 + x, 3, and $\frac{x^{2}+1}{y^{2}-1}$ are all expressions.

fission

A kind of morph in which a group of symbols is replaced with a larger group of symbols. Both groups must be mathematically equal to each other.

fusion

A kind of morph in which a group of symbols is replaced with a smaller or simpler group of symbols. Both groups must be mathematically equal to each other.

morph

A visual change in which an expression is replaced with a different expression. Both expressions must be mathematically equal to each other. Normally replacing the expression moves the equation closer to the solution.

multi-image

Used when solving plural equations. A multi-image is an image containing two or more whole equations, each coming from the same plural equation before its split. Each equation in the multi-image will lead to a solution of the equation.

operation

A symbol that signifies two expressions are being combined in some way to form another expression. +, -, $\times$ and $\div$ are operations.

plural

Describes an equation with multiple solutions, and which - at some point during the process of solving it - cannot be represented by a single equation (or simple image of an equation).

quantity

A number, variable, or expression of numbers and variables that can evaluate to a number.

relation

A symbol that signifies some quantitative relationship between two or more expressions. While the only relation discussed in this book is the equals sign (=), other examples are inequalities such as < or >.

singular

Describes an equation that can be solved by modifying an image of a single equation until it arrives at the solution.

split

A split is a point in the process of solving a plural equation in which it cannot be further solved using a single image, because multiple solutions have surfaced. Further processing (solving) requires the use of devices such as multi-images or subimages.

subimage

Used when solving plural equations. After a split in a plural equation, often the equations for each solution are similar except for a small sub-expression. A subimage is a portion of the larger image of the equation, usually containing only the sub-expression that is different. There will be two or more subimages, each containing a different sub-expression, and leading to a different solution of the equation.

symbol

A character or glyph that has some mathematical meaning. It can be a quantity, variable, relation, or operation.

symbol motion

A change in an image representing an equation or expression, which has a visual logic and produces a mathematical change in what is represented by the image. In particular, a symbol motion involves the movement or rearrangement of one or more symbols in the equation, with minor or no alterations. By definition, symbol motions honor the mathematical logic of the transformation. If some pattern does not preserve the mathematical logic, then it is not symbol motion.

visual logic

The systematic pattern of change in an image. Usually it means an image of an equation, and that the symbols in the image are moved or changed in a particular, abstract way.