Module 4: Mathematical Patterns

Question 1

a set of numbers arranged in some order

Answer 1

sequence

Question 2

ordered arrangement of a set of numbers

Answer 2

sequence

Question 3

a sequence of values that follows a pattern of adding a fixed amount (always the same) from one term to the next

Answer 3

arithmetic sequence

Question 4

the fixed amount in the arithmetic sequence is called

Answer 4

common difference

Question 5

the formula in the arithmetic sequence

Answer 5

an=a1+(n-1)d

Question 6

a sequence of values that follows a pattern of multiplying a fixed amount from one term to the next

Answer 6

geometric sequence

Question 7

the fixed amount in the geometric sequence

Answer 7

common ration, r

Question 8

the formula for finding the common ratio

Answer 8

r= an/an-1

Question 9

the formula for geometric sequence

Answer 9

an=an-1r or an=a1r^n-1

Question 10

a means of solving practical problems. sequence is formed by starting with 1,1 and adding the two preceding numbers to get the next number

Answer 10

Fibonacci Sequence

Question 11

who developed the fibonacci sequence

Answer 11

Leonardo Fibonacci

Question 12

examples of Fibonacci sequence in nature

Answer 12

nautilus shell, hurricane, galaxy

Question 13

the ratio of 2 successive Fibonacci numbers approach the number called

Answer 13

Golden Ratio

Question 14

the golden ratio is irrational and is noted by the ratio of…

Answer 14

(1+√5)/2 approx. 1.618

Question 15

involves flexible thinking, creativity, judgment, and logical problem-solving.

Answer 15

abstract reasoning

Question 16

refers to the ability to analyze information, detect patterns, and relationships and solve problems on a complex, intangible level.`

Answer 16

abstract reasoning

Question 17

factors to Compare in abstract reasoning

Answer 17

size, location, color, shades, angles, movement

Question 18

created when a shape or a combination of shapes are repeated over and over again covering a place without any gaps or overlaps using transformations; another word is

Answer 18

tessellation; tiling

Question 19

who were the first people who used tessellations; where did they put it

Answer 19

Sumerians at about 4000BC; build wall decorations in patterns of clay tiles

Question 20

some of the most famous tessellations

Answer 20

Moorish wall tiles of Islamic architecture

Question 21

became the first person to complete the study of tessellations after he explored the structure of honeycombs and snowflakes

Answer 21

Johannes Kepler

Question 22

300 years later, Russian crystallographer,_____, began the study of tessellations in mathematics.

Answer 22

Yvgraf Fyodorov

Question 23

methods used in tesselations

Answer 23

translation, rotation, reflection

Question 24

a tesselation made up of congruent regular polygons

Answer 24

regular tessellation

Question 25

3 regular polygons that tessellate in the Euclidian plane

Answer 25

triangles, squares, hexagons

Question 26

formed by regular polygons. the arrangement of polygons at every vertex is identical

Answer 26

semi-regular tessellations

Question 27

2 method of producing irregular shapes to tessellate

Answer 27

• translating (or sliding) the midpoint of any side of the starting shape making some curved lines
• rotating the midpoint of any side of the starting shape

Question 28

a world-famous graphic artist that attributed to the idea of transformation of shapes to create new, irregular, tessellating shapes

Answer 28

Mauritis Cornelis Escher (1898-1972)

Question 29

a rough or fragmented geometric shape that can be split into parts, each of which is approximately a reduced-size copy of the whole.

Answer 29

fractal

Question 30

amazingly complicated patterns often produced by very simple processes- reflection , rotation, and translation

Answer 30

fractals

Question 31

• demonstrate a fourth time of symmetry
• possess self-similarity

Answer 31

fractals

Question 32

a shape is _____ when it looks essentially the same from a distance as it does closer up.

Answer 32

self-similar

Question 33

a characteristic where an object is composed of smaller copies of itself

Answer 33

scaling symmetry or scale invariance

Question 34

fractals from mathematical constructions

Answer 34

Koch Curve; Sierpinski’s Triangle