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Mathematics

study of numbers and arithmetic operations. set of tools that can apply to "how many" or "how much"

Pattern

arrangement that helps observers anticipate what they might see.

1. Logic Pattem

first to be observed. involves classifying things & enumaration

2. Geometric Pattern

motif design that depicts abstract shapes like lines, circles (wallpaper)

3. Number Pattem

first pattern encountered in school

4. Word Pattern

Morphological miles on pluralizing nouns for tense.Pattern in form & syntax.

Fibonaca sequence

discovered by Leonardo Bonacci. 1,1,2,3,5,8,13,21,34, 55, 89, 121...

a. Liber albau (1202)

describe mathematics he learned

Golden Ratio

goes on forever. usually rounded to 3 decimal places. 1.618/1

a. Nature & Animals

nautilus shell

6. Music

organization of the sections in the Debussy Image.

c. Beauty

symmetrical face

Transformation

we can pair each point of a figure with exactly 1 point of a Euclidean plane

Reflection

mirrors a figure over a line.

Rotation

tums a figure at a certain point in a plane.

Translation

slides a figure in any particular direction

Glide Reflection

combination of translation & reflection

Frieze Pattern

has a pattern that repeats in one direction

a. Hop

only involves translation

Step+glide

reflection symmetry

C Siddle translation

translation+ VERTICAL reflection

a. Spinning Hop

translation but has rotation

e. Spinning siddle

translation, glide symm. & rotation

f. Jump

translation & horizontal reflection

Wallpaper Pattern

pattern w/ translation symmetrical in 2 directions. Arrangement of friezes

Tessellations or Tilling

pattern that repeats figures that cover a plane. no gasps & overlaps

Language

systematic means of communicating by sound & symbols. code humans use to express themselves.

Components

vocabulary, grammar, community of people.

Mathematics as Language

system of communication about members, variables, sets, etc. meaning shared by a global community

English

a. Noun name of object b. Sentence a complete thoragut

Mathematics

a. Expression name given to mathematical object (set, number) b. sentence a complete thought (21+4>0)

Characteristics of Mathematical Language

Precise, concise, Power ful

1. Precise

very fine destinctions / definitions (no ambiguity)

2. Concise

express long exposition briefly

3. Powerful

can repress complex thoughts with ease

Proposition

declarative sentence (can only be true or false only)

Tauntology

statement that is always true

Self contradiction

always false

Negation

NOT

Conjuction

and, white, but

Disjunction

or, either,

Conditional

if, them

Biconditional

if and only if