This document discusses the Fibonacci sequence, which was discovered by the Italian mathematician Leonardo Fibonacci in the 12th century. The sequence begins with 0, 1, 1, 2, 3, 5, etc., where each subsequent number is the sum of the previous two. The ratio of adjacent numbers approaches the Golden Ratio of approximately 1.618 as the sequence progresses. Examples are given of how the Fibonacci sequence and Golden Ratio appear throughout nature, such as in the spirals of shells, pinecones, sunflowers, and galaxies.
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Miracles of numbers
1.
2.
3.
4. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
Can you guess the next number in
this sequence?
89 + 144 = 233
5. FIBONACCI’S SEQUENCE
This sequence of numbers was first discovered
in the 12th century, by the Italian
mathematician, Leonardo Fibonacci, and
hence is known as Fibonacci's Sequence.
12. DNA molecule—
contains the golden
ratio. One revolution
of the double helix
measures 34
angstroms while the
width is 21 angstroms.
The ratio 34/21
reflects phi 34 divided
by 21 equals 1.619… a
close approximation
of phi’s 1.618.
13. Fibonacci numbers can be found
in many places, for example the
number of petals on a flower is
often a Fibonacci number.
1
2 3 5
13
8 13 21
14. People wonder…
Why is that the number of petals in a
flower is often one of the following numbers:
3,5,8,13,21,34,55?
15. Branching Plants
• Leaves are also found in
groups of Fibonacci
numbers.
• Branching plants always
branch off into groups
of Fibonacci numbers.
19. So, why do shapes that exhibit the Golden
Ratio seem more appealing to the human
eye? No one really knows for sure. But we
do have evidence that the Golden Ratio
seems to be Nature's perfect number.
20.
21. The front two incisor teeth form a
golden rectangle, with a phi ratio in the
height to the width.
The ratio of the width of the first tooth
to the second tooth from the center is
also phi.
The ratio of the width of the smile to the
third tooth from the center is phi as
well.
Asalamalaikum everyone. The topic of my presentation today is, Math, the Language of God, Miracles in Numbers. Now before I actually get on to the presentation, I would just like to mention something from the point of view of teaching. This topic is not in our Mathematics CIE syllabus. As a teacher, in class while teaching we face a lot of challenges and one of the challenges that I have faced is that every section I get, there is always a certain number of students who just hate the subject. And when I say hate, I really mean it, they hate it genuinely and they hate it with disgust and perhaps for even valid reasons. Because Math has been really cruel to them. Math has betrayed and insulted them over all the primary and lower secondary grades they have perhaps tried really hard and yet they have been getting Cs and DsThey might hate other subjects but I feel they will never hate it as much as Math.Now with these students who have been so disappointed with the subject and are lost and whatever you write on the board is gibberish to them, the problem is they don’t want to give the subject a second or third chance. And then there are some students who are even good at the subject but they object to the practicality of the subject about certain topicsSometimes it is important to scoop them out of the world of equations and mathematical notations and terminology and take them to a scenario which makes more sense to themSo now I am taking you away from these equations
Asalamalaikum everyone. The topic of my presentation today is, Math, the Language of God, Miracles in Numbers. Now before I actually get on to the presentation, I would just like to mention something from the point of view of teaching. This topic is not in our Mathematics CIE syllabus. As a teacher, in class while teaching we face a lot of challenges and one of the challenges that I have faced is that every section I get, there is always a certain number of students who just hate the subject. And when I say hate, I really mean it, they hate it genuinely and they hate it with disgust and perhaps for even valid reasons. Because Math has been really cruel to them. Math has betrayed and insulted them over all the primary and lower secondary grades they have perhaps tried really hard and yet they have been getting Cs and DsThey might hate other subjects but I feel they will never hate it as much as Math.Now with these students who have been so disappointed with the subject and are lost and whatever you write on the board is gibberish to them, the problem is they don’t want to give the subject a second or third chance. And then there are some students who are even good at the subject but they object to the practicality of the subject about certain topicsSometimes it is important to scoop them out of the world of equations and mathematical notations and terminology and give them a break. Introduce them to something that will make sense to them, that will make them appreciate the subjectTake you to something which requires no background knowledge. You start fresh. You start from a clean slate.So now I am taking you away from these equations
You have just tried to forge god’s signature
Now why is it called the Divine Proportion because a lot of things in nature occur in this proportion or in this sequence
http://www.world-mysteries.com/sci_17.htm
If you calibrate a plant at equal distances and you count the branches at each calibration, the branches will follow the Fibonacci Sequence
Common ratio in nature that made things appealing to the eye
The Parthenon was built on the Acropolis in Athens
Low pressure system over Iceland filmed from a satellite.
Furthermore, when one observes the heads of sunflowers, one notices two series of curves, one winding in one sense and one in another; the number of spirals not being the same in each sense. Why is the number of spirals in general either 21 and 34, either 34 and 55, either 55 and 89, or 89 and 144? The same for pinecones : why do they have either 8 spirals from one side and 13 from the other, or either 5 spirals from one side and 8 from the other? Finally, why is the number of diagonals of a pineapple also 8 in one direction and 13 in the other?