1. CENTENARY CELEBRATION P S HIGHER SECONDARY SCHOOL
P S HIGH SCHOOL NORTH
CENTENARY CELEBRATION
P S HIGHER SECONDARY SCHOOL
EXTENDS HEARTY
WELCOME

2. VENUE: P S SENIOR SECONDARY SCHOOL
DISTINGUISHED GUESTS
RESOUCE PERSONS
PARTICIPANTS
MATHEMATICS SEMINAR
DATE:9//1/16
VENUE: P S SENIOR SECONDARY SCHOOL

4. 1.To expose students beyond the boundaries of text books and
curriculum
2.To reduce abstraction
3.To relate mathematics to real life and nature
4.To look at a mathematical object from different perspective
5.To understand the effectiveness of technology in mathematic

5. Division of line

7. Demonstration using geogebra

8. Construction of golden ratio
on a straight line

9. Activity 1 1.Draw a line segment AB of any length
2.Draw a perpendicular at B
3.Bisect AB at C
4.With B as centre draw a circle of radius BC intersecting the perpendicular at B at D.
5.Join AD
6.Draw circle with center D radius BD intersecting AD at E.
7. Draw circle with center A and radius AE intersecting AB at F.
.Find AB/AF also AF/FB

10. 1.Compute AB/AF AF/FB without using scale and what do you observe.
2.what is the reason for drawing the perpendicular at B
3.What is the role each of the circles.

11. Demonstration using geogebra

12. Golden rectangle

13. Golden rectangle Activity 2 1.Construct a square ABCD
2.Let E be the mid point of AB
3.Draw a circle with E as centre and EC as radius to intersect AB produced to F
5.Draw the rectangle AFGD
6.This rectangle is knowns as the GOLDEN because the ratio of its sides s the golden ratio 𝝋≅𝟏.𝟔𝟏
AF/AD≅1.61

14. Find the ratio of length /Breadth. What you observe.
What is the significance of midpoint of the base of the square
Why do we construct a circle with CE as radius.

15. Demonstration using geogebra

20. GOLDEN TRIANGLE
1.Draw a line segment of length AB
2.Draw 72o at A and B to intersect at C
3. Bisect Angle A and B(angle bisectors of acute angles intersects at E and angle bisector of A intersect CB at E)
4.Draw triangles ABD and BED both are similar to triangle ABC
Find AC/AB

21. Why should be draw 72o
Why should be bisect angle A or B
What do you say about triangle ABD and ABC . or BED and ABC.

22. Demonstration using geogebra

24. Fibonacci introduced a sequence of natural numbers which are now
famously known as Fibonacci numbers
They are given by 1,1,2,3,5,8,13,21,
It can be easily seen that the nth number Fn in this sequence can be written as
Fn=Fn-1+Fn-2 for n≥𝟑

25. Drone is born out of a unfertilized larva (has a mother but no father)
REAL LIFE:
let us follow backward the ancestral family tree of a male honeybee(CALLED DRONE)
Drone is born out of a unfertilized larva (has a mother but no father)
Let M represent a male and F a female. M has only female ancestor where as F has both M and F.
M 1
F 1
M F 2
F MF 3
MF FMF 5
FMF MFMMF 8
No of petals in a large majority of flowers are Fibonacci numbers,

26. Fibonacci numbers appear in nature.
They appear in the arrangement of leaves in certain plants, on the patterns of the florets of a flower, the bracts of pinecone, and on the scales of a pineapple.
There are numerious examples of Fibonacci numbers and golden ratio in nature which students can explore in the form of project.

35. How to use excel to generate fibonnoci and golden ration

36. EXPLORING FIBONACCI NUMBERS USING EXCEL.
ACTIVITY 1
In column A create natural numbers from at A2 1 to 50.
In column B at B4 type =(B3+B2). We get Fibonacci series
Select B and insert chart/line to see the graph of Fibonacci series.
In column C at C3 enter =(B3/B2) and observe
Select C and insert chart/line
In column D on D4 type =(B4/B3) ( i.e)F_(n+1)/F_n
In column E at E3 type =(B3/B2) (i.e) F_n/F_(n-1)

37. GOLDEN SPIRAL

40. 1/8
In golden ratio its closely packed.

48. THANK YOU