Math prelims

Mathematics

science of numbers and their operations interrelations, combinations, generalizations, and abstractions and of space contigurations and their structuve, measurement, transformations, and generalizations

Counting

activity that leads to numbers, numerals,

addition, subtraction, multiplication, and division

Pattern

order, regulavity, and lawfulness. Observe, hypotesise, expermint, discover, and create. Arranged in a pattern.

Geometric shapes

motif/design depicting abstract, nonrepresentational shapes such as lines, circles, ellipses, triangles, rectangles and polygons. Consists of series of shapes

Logical pattern

Structured arrangement of ideas, numbers, or symbols that follow a consistent mule or reasoning process

Word pattern

Syntatic patterns of how we make nouns, plural of verbs, past tense. Patterns of words that are wade up of both consonants and vowels.

Packing problem

Finding the optimum method of filing up a given space such as cubic or spherical container

General formula

Area of the circle / area of the square x 100%

Area of each triangle

A = side² x√3/ 4

Area of a hexagon

Area of the circle /area of the hexagon x 100%

Chaos theory

deals with non linear things that effectively impossible to predict or control. Things to look random.

ex: Weather, motion of fluid, smoke, ocean currents

Fractals

Never ending pattern. Infinitely complex patterns trat are self-similar across different scales. An ongoing loop ex: pineapple, leaves, broccoli, clouds, snowflakes

Fibonacci sequence

Integer in the infinite sequence 1, 1 ,2, 3, 5, 8, 13,... of which the two terms are 1 and 1 and each succeeding term is the sum of the two immediately preceding

Leonardo pisano

Real name of fibonaccii

1170

Leonardo pisano was born on 1170

1250

Leonardo pisano died at 1250

Pisa

Where leonardo died now called italy

North africa in mathematics

he studied at

Liber abaci, parrica, geometriae, liber quadratorum

Wrote books

Rabbit problem

Talks about breeding process of rabbits. Total number of rabitts in a month is equal to the total pairs of rabbits in the previous month

Symmetry

you can draw an imaginary line across an object and the resulting parts are minor images of each other

Bilateral

Object divided into 2 halves

Radical

Divided into similar parts by more than 2 planes (starfish, 4 leaf clover)

Fivefold

Five identical parts (starfish)

Sixfold

Object looks the same after being rotated by 60 degrees around the central axis. Ex: snowflakes, honeycomb

Symmetry

a rotational symmetry of order n (n-fold rotational symmety) if 1/n of a complete turn leaves the figure unchanged

360/n

Angle of rotation

Golden ratio

represented by greek letter Φ "Phi"

equal to 1. 618.

- made by dividing a line into two parts in such a way that the longer part divided by the shorter part, and the whole length divided by the longer part are both equal to 1.618

A/b = a+b/a = 1.618

Golden ratio formula