Reviewer 1

Question 1

What is mathematics?

Answer 1

A branch of science dealing with numbers and their operations, involving calculation, computation, and problem-solving.

Mathematics is defined as the science of numbers and space, measurement, quantity, and magnitude.

Question 2

What is a pattern?

Answer 2

An arrangement that helps observers anticipate what they might see or what happens next.

Question 3

According to the National Council of Teachers of Mathematics, what defines the nature of mathematics?

Answer 3

A study of patterns and relationships, a way of thinking, an art, a language, and a tool.

Question 4

What is symmetry?

Answer 4

Congruence in dimensions, due proportions, and arrangement, providing a sense of harmony and balance.

Question 5

What is bilateral or reflection symmetry?

Answer 5

The simplest kind of symmetry where a shape can be folded in half to fit exactly on top of the other.

Also known as mirror symmetry.

Question 6

What is a line of symmetry?

Answer 6

A fold that divides a shape into two equal parts.

Question 7

What defines radial symmetry?

Answer 7

Rotational symmetry around a fixed point known as the center.

Question 8

What are rosette patterns?

Answer 8

Patterns formed by rotating and/or reflecting a motif or element.

They can be cyclic (only rotational symmetries) or dihedral (both rotational and bilateral symmetries).

Question 9

What is a frieze pattern?

Answer 9

A pattern in which a basic motif repeats itself in one direction, extending to the left and right.

Question 10

What type of symmetry does a ‘Hop’ frieze pattern admit?

Answer 10

Only translational symmetry.

Question 11

What type of symmetry does a ‘Step’ frieze pattern admit?

Answer 11

Translational and glide symmetries.

Question 12

What type of symmetry does a ‘Sidle’ frieze pattern admit?

Answer 12

Translational and vertical reflection.

Question 13

What type of symmetry does a ‘Spinning Hop’ frieze pattern admit?

Answer 13

Translational and 180 rotations.

Question 14

What type of symmetry does a ‘Spinning Sidle’ frieze pattern admit?

Answer 14

Translational, vertical reflections, rotations, and glide reflections.

Question 15

What type of symmetry does a ‘Jump’ frieze pattern admit?

Answer 15

Translational, horizontal reflection, and glide reflections.

Question 16

What type of symmetry does a ‘Spinning Jump’ frieze pattern admit?

Answer 16

Translations, vertical reflections, horizontal reflections, rotations, and glide reflections.

Question 17

What is a wallpaper pattern?

Answer 17

A pattern with translation symmetry in two directions, consisting of reflection, rotation, and glide reflection symmetries.

There are only 17 distinct types of wallpaper patterns.

Question 18

What is a tessellation?

Answer 18

A repeating pattern of figures that covers a plane with no gaps or overlaps.

Question 19

Who invented the Fibonacci sequence?

Answer 19

Leonardo Pisano Bigollo (1180-1250).

Question 20

What is the Golden Ratio?

Answer 20

ϕ = Approximately 1.618.

Question 21

What is a proposition?

Answer 21

A declarative sentence that can be objectively identified as either true or false.

Question 22

What is negation in terms of a proposition?

Answer 22

The proposition which is false when p is true and true when p is false, denoted by ¬p.

Question 23

What is conjunction in logical terms?

Answer 23

The proposition ‘p and q’, denoted by p ∧ q, which is true only when both p and q are true.

Question 24

What is disjunction in logical terms?

Answer 24

The proposition ‘p or q’, denoted by p ∨ q, which is false only when both p and q are false.

Question 25

Fill in the blank: A ________ is a repeating pattern of figures that covers a plane with no gaps or overlaps.

Answer 25

tessellation.