Reviewer 1 Flashcards
(25 cards)
What is mathematics?
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.
What is a pattern?
An arrangement that helps observers anticipate what they might see or what happens next.
According to the National Council of Teachers of Mathematics, what defines the nature of mathematics?
A study of patterns and relationships, a way of thinking, an art, a language, and a tool.
What is symmetry?
Congruence in dimensions, due proportions, and arrangement, providing a sense of harmony and balance.
What is bilateral or reflection symmetry?
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.
What is a line of symmetry?
A fold that divides a shape into two equal parts.
What defines radial symmetry?
Rotational symmetry around a fixed point known as the center.
What are rosette patterns?
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).
What is a frieze pattern?
A pattern in which a basic motif repeats itself in one direction, extending to the left and right.
What type of symmetry does a ‘Hop’ frieze pattern admit?
Only translational symmetry.
What type of symmetry does a ‘Step’ frieze pattern admit?
Translational and glide symmetries.
What type of symmetry does a ‘Sidle’ frieze pattern admit?
Translational and vertical reflection.
What type of symmetry does a ‘Spinning Hop’ frieze pattern admit?
Translational and 180 rotations.
What type of symmetry does a ‘Spinning Sidle’ frieze pattern admit?
Translational, vertical reflections, rotations, and glide reflections.
What type of symmetry does a ‘Jump’ frieze pattern admit?
Translational, horizontal reflection, and glide reflections.
What type of symmetry does a ‘Spinning Jump’ frieze pattern admit?
Translations, vertical reflections, horizontal reflections, rotations, and glide reflections.
What is a wallpaper pattern?
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.
What is a tessellation?
A repeating pattern of figures that covers a plane with no gaps or overlaps.
Who invented the Fibonacci sequence?
Leonardo Pisano Bigollo (1180-1250).
What is the Golden Ratio?
ϕ = Approximately 1.618.
What is a proposition?
A declarative sentence that can be objectively identified as either true or false.
What is negation in terms of a proposition?
The proposition which is false when p is true and true when p is false, denoted by ¬p.
What is conjunction in logical terms?
The proposition ‘p and q’, denoted by p ∧ q, which is true only when both p and q are true.
What is disjunction in logical terms?
The proposition ‘p or q’, denoted by p ∨ q, which is false only when both p and q are false.
