Mathematics in the Modern World – Patterns & Nature

Fill-in-the-blank flashcards covering definitions, algebraic identities, symmetry types, and notable natural patterns discussed in the lecture notes.

Mathematics is a __ that makes use of symbols and notations for describing relationships.

language

Mathematics is a human activity that involves observing, representing and investigating __ in phenomena.

patterns

In radial symmetry, the angle of rotation is found by dividing __° by the number of folds.

360

Drawing an imaginary line that forms two equal halves of an object refers to __ symmetry.

bilateral

A __ is defined as a regular, repeated or recurring form or design.

pattern

Snowflakes exhibit natural __ symmetry, creating sixfold patterns.

radial

The honeycomb is built from a repeating __ lattice structure.

hexagon

Honeycomb construction demonstrates efficient space __ for storing honey.

packing (or optimization)

Animal stripes and spots are biological patterns primarily used for __.

camouflage

Tigers, zebras and okapis show __ patterns on their bodies.

stripe

Leopards and hyenas display body patterns of __.

spots

Wave formations in oceans, sand dunes, and stalactites are examples of natural __ in Earth’s landscapes.

patterns

The mathematical constant π is commonly approximated as __.

3.14

The Pythagorean theorem is expressed as __.

a² + b² = c²

The algebraic identity a² – b² = __.

(a + b)(a – b)

In exponents, a^m × a^n = a^{__}.

m + n

To find hidden relationships, mathematicians first __, then represent, and finally interpret patterns.

find (or observe)