MATHEMATICS IN THE MODERN WORLD What is mathematics

MATHEMATICS IN THE MODERN WORLD

What is mathematics? Formal system of thought for recognizing, classifying, and exploiting patterns The origins of counting Geometric patterns Wave patterns in water and on land Patterns of movement Fractals

Where is mathematics? We see hints or clues of it … In nature In our daily routine In our world In people and communities In events

What is mathematics for? To help us unravel the puzzles of nature, a useful way to think about nature Organize patterns and regularities as well as irregularities To be able to predict To help us control weather, epidemics Provides tools for calculations Provides new questions to think about

What is mathematics about? Numbers, symbols, notations Operations, equations, and functions Processes and “thingification” of processes (that are abstractions, e. g. , 3) Proof – a story rather than a sequence of statements

How is mathematics done? With curiosity With a penchant for seeking patterns and generalities With a desire to know the truth With trial and error Without fear of facing more questions and problems to solve With tenacity (willingness to keep working)

Who uses mathematics? Mathematicians: pure and applied Scientists: natural and social Practically everyone But different people use different math at different times, for different purposes, using different tools with different attitudes

Why is mathematics important to know? It puts order in disorder It helps us become better persons It helps the world a better place to live in

Name: Leonardo Bonac Popularly known as FIBONACCI Also known as. . . Leonardo of Pisa Leonardo Pisano Bigollo Leonardo Fibonacci Born: 1170, Pisa, Italy Died: 1250, Pisa, Italy Most talented mathematician of the middle ages

In 1202, Fibonacci wrote a very famous book “Liber abaci” to describe mathematics he learned. If two new be in the rabbits are pen after put in a pen, one year? How many rabbits will

“If 2 new born rabbits are put in a pen, how many rabbits will be in the pen after one year? ” Assume that rabbits. . . always produce one male and one female offspring. . can reproduce once every month. . can reproduce when they are one month old. . never die! Your Task: Work with your seatmate and create an illustration (tree diagram, table, flowchart, etc) on how the rabbit population expanded over a year.

http: //britton. disted. camosun. bc. ca/fibslide/fib 00. jpg

White Calla Lily: http: //britton. disted. camosun. bc. ca/fibslide/fib 01. jpg

Euphorbia: http: //britton. disted. camosun. bc. ca/fibslide/fib 02. jpg

Trillium: http: //britton. disted. camosun. bc. ca/fibslide/fib 03. jpg

Columbine: http: //britton. disted. camosun. bc. ca/fibslide/fib 04. jpg

Bloodroot: http: //britton. disted. camosun. bc. ca/fibslide/fib 05. jpg

Black-eyed susan: http: //britton. disted. camosun. bc. ca/fibslide/fib 06. jpg

Shasta Daisy with 21 petals: http: //britton. disted. camosun. bc. ca/fibslide/fib 07. jpg

Field daisies with 34 petals: http: //britton. disted. camosun. bc. ca/fibslide/fib 08. jpg

The Fibonacci sequence in plants Count the number of branches per generation.

The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . . How many rabbits are there on the 13 th month? 14 th month? Can you state the rule on how to get a term of the sequence?

The Fibonacci SURPRISE! 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . . What can you say about every third term? What can you say about every fourth term? What can you say about every fifth term?

MORE SURPRISES! 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . . Try adding together any three consecutive Fibonacci numbers. What do you notice? Can you explain it? Choose any four consecutive Fibonacci numbers. Add the first and last, and divide by two. What do you notice? Can you explain it? Discover any surprise of your own.

Fruits A banana has 3 sections An apple has 5 sections Fabulous Fibonacci: http: //fabulousfibonacci. blogspot. com/

Pineapple Fabulous Fibonacci: http: //fabulousfibonacci. blogspot. com/

Cauliflower Fabulous Fibonacci: http: //fabulousfibonacci. blogspot. com/

http: //www. gettyimages. com/detail/photo/cone-of-pine-royalty-free-image/108820976

http: //www. gettyimages. com/detail/photo/top-view-of-a-brown-pine-cone-on-a-white-

http: //www. gettyimages. com/detail/photo/hawaii-oahu-diamond-head-sunflower-close-uphigh-res-stock-photography/601204276

https: //www. 123 rf. com/photo_7987120_sunflower-seedheaad-pattern-fibonacci. html

https: //www. shutterstock. com/image-photo/lily-flowers-on-white-background 252724396? irgwc=1&utm_medium=Affiliate&utm_campaign=Nguyen%20 Duy%20 Phi&utm_sou

http: //www. gettyimages. com/detail/photo/buttercups-summer-sun-royalty-freeimage/172368337

http: //www. gettyimages. com/detail/photo/close-up-of-yellow-back-eyed-susan-flower-royaltyfree-image/562845269

http: //www. gettyimages. com/detail/photo/close-up-of-beautiful-dutch-iris-royalty-freeimage/159594206

http: //www. gettyimages. com/detail/photo/aster-royalty-free-image/185089362

http: //www. gettyimages. com/detail/photo/yellow-cauliflower-royalty-free-image/186828825

http: //www. gettyimages. com/detail/photo/yellow-cauliflower-royalty-free-image/186828825

https: //www. noupe. com/inspiration/photography/nature-s-pattern-photography-35 -outstanding-photos. html

https: //www. noupe. com/inspiration/photography/nature-s-pattern-photography-35 -outstanding-photos. html

https: //www. noupe. com/inspiration/photography/nature-s-pattern-photography-35 -outstanding-photos. html

https: //www. noupe. com/inspiration/photography/nature-s-pattern-photography-35 -outstanding-photos. html

http: //www. gettyimages. com/detail/photo/bees-royalty-free-image/157643400 https: //www. extremetech. com/extreme/172357 -the-most-beautiful-snowflake-photos-youll-ever-see-captured-with-acheap-diy-camera