Intro and Patterns and Numbers in Nature

man-made designs

(geometric patterns) -symmetric designs of bridge supports. -wind mills -house roofs -church inferior designs

natural occurences

(geometric patterns) -vibrant designs of flowers and leaves of certain plants. -fascinating designs in the skin of some animals. -cloud formations

fibonacci sequence (numbers)

(numeric pattern) 1,1,2,3,5,8,13,21 -is a series of number is found by adding up two numbers before it. Starting with 0 and 1, the seuqnce goes. -the succeeding numbers in the sequence are determined by adding two previous numbers. -paved the way to quantify observable patterns like the golden angle, golden ratio, golden rectangle(traingle)

velocity, speed

(pattern of change) -describes how distance is changing with time.

acceleration

(pattern of change) -how velocity changes with time.

patterns

-are the most fundamental feature of mathematics. -have conceivably evolved to new perspectives bringing about a more relevant approach in modeling the processes that are taking place in the natural world.

hairyball theorem

-even if we smoothen a specific surface there will be a certain point where the chaos will happen.

Leonardo Pisano

-introduced the fibonacci numbers -he started with a newly-born pair (male and female) of rabbits which are able to mate after on month,

mathematics

-is all about patterns, pursued at varying levels of abstractions and the relationships that are exhibited in them. -it is a language which thrives in its unique yet universal symbolisms, serving as the grammar of scientific ideas and the ultimate expression of the grandeur of creation. -it is a powerful tool to understand and explain almost all phenomena that occur in nature and in the world and many more... -can be considered as the science of patterns

philippine setting

-mt.Mayon -chocolate hills in Bohol -Sand dunes in Ilocos -Textile designs associated with various Filipino ethnic communities -architectural designs -church interior designs.

the system of mathematics

-one's understanding of the universe continues to reach greater and mathematics is rightfully credited for this.

patterns of change

-relates to the change of one variable to another variable.

geometric patterns

-shapes

chaos

-superficial randomness originating from deterministic behavior, on the principle that even with seemingly chaotic pattern, a sense of repetition and periodicity. -weather conditions -celestial mechanics -population models (bacteria) -predictive modeling.

difference method

-take the difference of a number subtracted bu the preceeding number.

fractal

a type of random pattern with each part having te same characteristic as the whole. -mountain formation and erosion -wind flows -crystal structures -branching of trees -self replicating design

137.5

golden angle

1.618/1.62

golden ratio

types of patterns

numeric patterns