Lecture Note 5 Flashcards
Decimals which are _________________ and _________________________ are
classified to be irrational
non-terminating, non-repeating
is a special number approximately equal to 1.618
golden ratio
A number which cannot be expressed as a ratio between two integers is
called an?
irrational number
this happens when you break up a circle so that the ratio of the big arc to the little arc is the Golden Ratio
golden angle
for everyday writing
xiaxie
are considered magical values in the sense that they consistently and inexplicably appear in nature like leaves, flowers, fruits, and shells
fibonacci number and golden ratio
is a real multiple of i
imaginary number
The union of the set of rational and irrational numbers is the?
set of real numbers
It is like taking the line definition of the Golden Ratio and wrapping it into a circle
golden angle
if it is different from 1 and is not composite
prime number
equal to the number of positions that preserves the figure when it is repeatedly rotated θo until it reaches one revolution.
order of rotation
The next number is found by adding up the two numbers before it.
fibonacci numbers
can be drawn in its entirety by taking a portion of the figure and shifting it along an axis.
translational symmetry
One of the most interesting number patterns
pascal’s triangle
This system satisfies all axioms discussed before except the last (Existence of Multiplicative Inverse)
modular system
is the most basic way of assigning symbols to quantity
tally marks
are usually understood symbols, more so than letters, that are often used to convey mathematical
numbers
points on it are uniformly situated around a point that serves as center of the object
radial symmetry or rotational symmetry
it tells us that changing the order of the given, both for addition and multiplication, does not affect the result
commutativity
sliding of an object about an axis
translational symmetry
The bigger the pair of ______________, the closer the approximation
Fibonacci
For any pair of real numbers a and b, their sum (a + b) and product (ab) are also real numbers.
closure
separates the figure into equal parts, and it serves as a mirror to half of the figure
axis of symmetry
At around 3000 BC, Egyptians had a numeration system which used special symbols called?
hieroglyphs
A strip with a symmetric pattern
frieze pattern
pascal triangle is named after
blaise pascal
it is a statement or proposition which is regarded as being established, accepted, or self-evidently true
axiom
The Babylonians inherited ideas for a base 60 system referred to as the?
sexagesimal system
The smallest angle that would preserve the figure when rotated
There are _______________ possible Frieze patterns provided that the design is
one color
seven
it is different from 1
and can be expressed as the product of two or more positive integers different from itself
composite number
The rectangle formed by making adjacent squares of Fibonacci dimensions is called the?
golden rectangle
A number system which has its base as ”eight” is called an
octal system
An ever repeating pattern of triangles
sierpinski triangle
it tells us that, without changing the order, the sum and product will still be the same regardless of which pair of given is considered first
associativity
points of the figure are equally positioned about a line
reflectional symmetry
two sets of characters for chinese numerals
xiaoxie and daxie
for commercial or financial writing
daxie
it is a number that can be expressed as a ratio of two integers, where the denominator is non-zero
rational number
it is the study of encoding and decoding messages
cryptopgrahy
is a type of number system, that has a base value equal to 16
hexadecimal number system
When we take any two successive Fibonacci numbers, their ratio is
very close to the
golden ratio
refers to a decorative carving or pattern that runs horizontally just below a
roofline or ceiling.
frieze
For any pair of real numbers a and b, their sum and product give the same result even if the elements combined are swapped, i.e.,
commutativity
is a combination of a real number and an imaginary number of the form z = a + bi
complex number
