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21 Cards in this Set

  • Front
  • Back

Ishango Bone (20k yrs ago)

Counting started Unified series of unified lines cut into bone

Programma 101 (1965)

First personal desktop computer

Apollo 11 (1969)

First landing of man on the moon

GPS (1989)

Benefit military at first

1. Distance between u and each of these satellites


2. Location of atleast 3 satellites above you

Calculation of GPS

1. Geometric patterns


2. Wave patterns


3. Patterns of movement


4. Fractals

Patterns

Fractals

Mathematical formula of a pattern

Benoit Mandelbrot

Father of fractals

1. Flower petals


2. Honeycomb


3. The sunflower


4. Snowflakes


5. Snail's shell

Fibonacci patterns examples

34 - clockwise


21 - counter clockwise

Sunflower fibonacci number

Mathematics

Formal system of thought for recognizing, classifying, and exploiting patterns

Topology

Study of properties of shapes that stay the same after continuous deformation

Cowlicks

Example of topology that Persists even after stretching, bending, twisting

1. Organize patterns, regularities, and irregularities


2. Pythagoras proclaimes that nature was numbers


3. To be able to predict


4. Help us to forecast weather conditions


5. Help us to Control epidemics


6. Provide tools for calculations


7. Provide new questions to think about

Purposes of mathematics

Fibonacci sequence

Sequence beginning with 1,each subsequent number is the sum of the two proceding numbers

1. Fibonacci in sunflowers


2. Fibonacci in pineapples


3. Fibonacci in plants


4. Fibonacci numbers in nature


5. Fibonacci in animals

Examples of Fibonacci sequence found in nature

Golden ratio (1.618033...)


-aka Golden mean, divine proportion, golden proportion

-known by many other names such as...


-Represented by Greek letter Phi


-defined by Greek mathematician Euclid in 300 BC





Base = 1


Height = √phi


Slant height = Phi

Great pyramid of Giza

The Parthenon

The exterior dimensions form a Golden Ratio

1. With a desire to know the truth


2. With trial and error

How is mathematics done?

1. Pure and applied mathematicians


2. Natural scientists


3. practically everyone


Who uses mathematics?