Informative Speech Outline
Name: Dijesh Pradhan
Presentation Title: Fibonacci Numbers and The Golden Ratio
Purpose: To inform my audience about Fibonacci numbers and the golden ratio so that they will be able see the how and why these numbers appear in nature.
Introduction:
What do you think is interesting about the picture of sunflower? Who can predict the number of petals in the sunflower and the number of spirals in this flower? The number of petals is 34 and the number of spirals is 55 in each direction (clockwise and anticlockwise). What if at the end of the presentation all of you could predict these. In order to do that we need to learn about the Fibonacci numbers. I am a Computer engineering major student doing minor in Mathematics. I have a great interest in mathematics and fascinated with numbers. So, I would love to discuss about my favorite number Fibonacci numbers. Many of us think that the problems and formula that we learn in mathematics is important for the next class or something that we will learn in the next chapter. But what if we learn mathematic for something useful, knowing the use of the applications of the things that we are learning. After knowing about these numbers, you will not only know how these numbers are everywhere in the nature but also the beauty that mathematics has.
Body
I. Fibonacci numbers are that evoke the power and beauty of mathematics and is found by adding numbers starting from 1 to its previous number (Alfred, 2007)
A. Fibonacci numbers: These numbers are made by adding a number to its previous number. The process was discovered by Indians 1300 years before and was introduced in the west by an Italian mathematician Leonardo Pisano which was described in his book Liber Abaci.
1. So, we start from 1 and add it to 0 which will give us 1, and then we add 1 with 1 which will give us 2, and add 2 with 1 and get 3, add 3 with 2 and get 5 and keep following this process.
B. The Golden Ratio: The golden ratio is an irrational number, meaning it is a number that cannot be obtained by dividing one number by another. To find this number, we keep dividing one Fibonacci number by the preceding number in the Fibonacci sequence and if we repeat this process, we get closer and closer to a number, i.e. 1.618… and this is the golden ratio. The number is pronounced as phi and one of its properties is that it is the most irrational number (Mario, 2002).
II. The most important thing for a plant is to grow leaves and flowers(petals) in such a way that they can trap the maximum amount of sunlight and grow the maximum amount of seeds in the amount of space that they have got.
A. Plants are dumb, and they certainly do not know any Mathematics and there are 360 degrees where the plant can grow a seed.
B. Let’s say there is one seed and the next seed is grown at an angle of 180 degrees then we just get 2 lines of seed and the plant will waste a bunch of available space.
C. Dividing the 360 degrees that the plant has to grow a seed by any rational number (a number which can be written as a fraction e.g. 5 = 10/2) will not work and after a certain amount of times, the pattern will repeat, and a bunch of available space will be wasted.
D. But, dividing the 360 degrees by an irrational number (e.g. pi, Rt2) will produce better results. So, we divide 360 degrees by the most irrational number which is the golden ratio (1.1618….), it will get 222.5 degrees /137.5 degrees depending if we look from counterclockwise direction or clockwise direction.
E. If the plant grows the next seed at an angle of 137.5 degrees to the previous seed, it will utilize all the space and the spiral pattern, and the number of Fibonacci petals emerges by itself (The Fibonacci Sequence, 2014). So, all a plant got to do is grow every petal, seed, leaf at an angle of 137.5 degrees to the previous petal, seed or leaf. A method so simple that even plant can do it.
III. There are various uses of these numbers, from being used in the stock market, to photography to architecture to design.
A. In photography, the golden ratio is used to make grids such that if we keep the object that we are taking the photo of in the intersection of the lines of the grids, we will almost always get a good photo.
B. Famous logos like logos of National Geographic, Pepsi, Mercedes Benz, etc. is made by the use of the golden ratio.
C. Fibonacci sequence is used in stock market and it can also be used to convert from miles to kilometers.
Conclusion:
Mathematics is beautiful, and we are surrounded by numbers and patterns that emerge out of these numbers. Phi and Fibonacci numbers are just some of these numbers, simple numbers that have such complex consequences, that can create these spirals in plants, and rules that every plant can follow. I will end with a quote by Arthur Benjamin. “Mathematics is not just solving for X, it is also about finding out why.” (Arthur, 2015)
References
Alfred S. Posametier (2007). Numbers that evoke the power and beauty of Mathematics. The Fabulous Fibonacci Numbers, pg. 15.
Leonardo Pisano a.k.a Fibonacci (1202). Liber Abaci, section 3. Retrieved from http://www-history.mcs.st-andrews.ac.uk/Biographies/Fibonacci.html
Mario Livio. (2002). The Golden Ratio, The story of PHI, the world’s most astonishing number. The Divine Proportion. 6(3): 125-127
The Fibonacci Sequence. (2014). Protea Atlas Project. Retrieved from
https://www.proteaatlas.org.za/fibon.html
Arthur T Benjamin. (2015). The Magic of Math: Solving for x and Figuring Out Why. 4(2): 75-76