Mathematics in Our World and Mathematical Language

Vocabulary flashcards covering patterns in nature, applications of math, mathematical language characteristics, mathematical expressions versus sentences, and logical connectives.

Pattern

Any sequence or design in nature that is orderly and repeats, or more broadly, anything that is not random.

Symmetry

A structural property where different sides of something are alike, such as mirror images with two sides, symmetry on several sides, or symmetry on all sides.

Six-fold Symmetry

The specific symmetrical structure exhibited by snowflakes.

Fractals

'Never-ending' patterns that repeat indefinitely as the pattern is iterated on an infinitely smaller scale, such as in trees, rivers, mountains, leaves, and lightning.

Spirals

A common pattern in nature seen more often in living things, such as sheep horns, nautilus shells, and leaf arrangement around a stem.

Logarithmic Spiral

A special type of spiral that gets smaller as it goes, observed in hurricanes, galaxies, and some seashells.

Fibonacci Sequence

The sequence of numbers $1, 1, 2, 3, 5, 8, 13, 21\text{...}$ where each number is the sum of the two numbers before it.

Drone (Honeybee Colony)

A male honeybee that hatches from an unfertilized egg, having $1$ parent, $2$ grandparents, $3$ great-grandparents, following a Fibonacci pattern.

Tessellations

Patterns formed by repeated cubes or tiles in living and non-living things, such as floor tiles, brick walks, and honeycombs.

Language

A complex system of words and symbols, either spoken or written, used by a particular community as a means of communication.

Precise (Language of Mathematics)

A characteristic of mathematical language referring to its ability to make very fine distinctions.

Concise (Language of Mathematics)

A characteristic of mathematical language referring to its ability to say things briefly.

Powerful (Language of Mathematics)

A characteristic of mathematical language referring to its ability to express complex thoughts with relative ease.

Expression

The mathematical analog of an English noun; a correct arrangement of mathematical symbols that names an object of interest and does not state a complete thought.

Mathematical Sentence

The mathematical analog of an English sentence; a correct arrangement of mathematical symbols containing a verb that states a complete thought.

Radical Symbol

The symbol \text{\sqrt{}} used to denote a square root.

First Meaning of 'Is' (Equality)

The use of the word 'is' in mathematics meaning 'equals' or asserting that two expressions represent one and the same object, as in '$5$ is the square root of $25$'.

Second Meaning of 'Is' (Property)

The use of the word 'is' in mathematics to attach an adjectival phrase specifying a property that objects may or may not have, as in '$5$ is less than $10$'.

Third Meaning of 'Is' (Example of)

The use of the word 'is' in mathematics meaning 'is an example of' or indicating set membership, as in '$5$ is a prime number'.

Negation

A statement formed by denying or expressing the opposite of an original statement.

Conjunction

A compound sentence formed by using the word 'and' to join two simple sentences, symbolized as $p \wedge q$.

Disjunction

A compound sentence formed by using the word 'or' to join two simple sentences, symbolized as $p \vee q$.

Implication

A relationship between two statements symbolized by $p \Rightarrow q$ ('if $p$ then $q$'), meaning that if $p$ is true, then $q$ must also be true.

Premise

The initial statement $p$ in an implication statement $p \Rightarrow q$.

Conclusion

The resulting statement $q$ in an implication statement $p \Rightarrow q$.