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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
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
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.
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
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.
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
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.
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
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
F
MF
F
MF
FMF
MF
FMF
MFMMF
1
1
2
3
5
8
No of petals in a large majority of flowers are Fibonacci numbers,
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.
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)
1/8
In golden ratio its closely packed.