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
