Lecture Note 5

Question 1

Decimals which are _________________ and _________________________ are
classified to be irrational

Answer 1

non-terminating, non-repeating

Question 2

is a special number approximately equal to 1.618

Answer 2

golden ratio

Question 3

A number which cannot be expressed as a ratio between two integers is
called an?

Answer 3

irrational number

Question 4

this happens when you break up a circle so that the ratio of the big arc to the little arc is the Golden Ratio

Answer 4

golden angle

Question 5

for everyday writing

Answer 5

xiaxie

Question 6

are considered magical values in the sense that they consistently and inexplicably appear in nature like leaves, flowers, fruits, and shells

Answer 6

fibonacci number and golden ratio

Question 7

is a real multiple of i

Answer 7

imaginary number

Question 8

The union of the set of rational and irrational numbers is the?

Answer 8

set of real numbers

Question 9

It is like taking the line definition of the Golden Ratio and wrapping it into a circle

Answer 9

golden angle

Question 10

if it is different from 1 and is not composite

Answer 10

prime number

Question 11

equal to the number of positions that preserves the figure when it is repeatedly rotated θo until it reaches one revolution.

Answer 11

order of rotation

Question 12

The next number is found by adding up the two numbers before it.

Answer 12

fibonacci numbers

Question 13

can be drawn in its entirety by taking a portion of the figure and shifting it along an axis.

Answer 13

translational symmetry

Question 14

One of the most interesting number patterns

Answer 14

pascal’s triangle

Question 15

This system satisfies all axioms discussed before except the last (Existence of Multiplicative Inverse)

Answer 15

modular system

Question 16

is the most basic way of assigning symbols to quantity

Answer 16

tally marks

Question 17

are usually understood symbols, more so than letters, that are often used to convey mathematical

Answer 17

numbers

Question 18

points on it are uniformly situated around a point that serves as center of the object

Answer 18

radial symmetry or rotational symmetry

Question 19

it tells us that changing the order of the given, both for addition and multiplication, does not affect the result

Answer 19

commutativity

Question 20

sliding of an object about an axis

Answer 20

translational symmetry

Question 21

The bigger the pair of ______________, the closer the approximation

Answer 21

Fibonacci

Question 22

For any pair of real numbers a and b, their sum (a + b) and product (ab) are also real numbers.

Answer 22

closure

Question 23

separates the figure into equal parts, and it serves as a mirror to half of the figure

Answer 23

axis of symmetry

Question 24

At around 3000 BC, Egyptians had a numeration system which used special symbols called?

Answer 24

hieroglyphs

Question 25

A strip with a symmetric pattern

Answer 25

frieze pattern

Question 26

pascal triangle is named after

Answer 26

blaise pascal

Question 27

it is a statement or proposition which is regarded as being established, accepted, or self-evidently true

Answer 27

axiom

Question 28

The Babylonians inherited ideas for a base 60 system referred to as the?

Answer 28

sexagesimal system

Question 29

The smallest angle that would preserve the figure when rotated

Question 30

There are _______________ possible Frieze patterns provided that the design is one color

Answer 30

seven

Question 31

it is different from 1 and can be expressed as the product of two or more positive integers different from itself

Answer 31

composite number

Question 32

The rectangle formed by making adjacent squares of Fibonacci dimensions is called the?

Answer 32

golden rectangle

Question 33

A number system which has its base as ”eight” is called an

Answer 33

octal system

Question 34

An ever repeating pattern of triangles

Answer 34

sierpinski triangle

Question 35

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

Answer 35

associativity

Question 36

points of the figure are equally positioned about a line

Answer 36

reflectional symmetry

Question 37

two sets of characters for chinese numerals

Answer 37

xiaoxie and daxie

Question 38

for commercial or financial writing

Answer 38

daxie

Question 39

it is a number that can be expressed as a ratio of two integers, where the denominator is non-zero

Answer 39

rational number

Question 40

it is the study of encoding and decoding messages

Answer 40

cryptopgrahy

Question 41

is a type of number system, that has a base value equal to 16

Answer 41

hexadecimal number system

Question 42

When we take any two successive Fibonacci numbers, their ratio is very close to the

Answer 42

golden ratio

Question 43

refers to a decorative carving or pattern that runs horizontally just below a roofline or ceiling.

Answer 43

frieze

Question 44

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.,

Answer 44

commutativity

Question 45

is a combination of a real number and an imaginary number of the form z = a + bi

Answer 45

complex number