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

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

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

Division of line

Demonstration using geogebra

Construction of golden ratio on a straight line

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.

Demonstration using geogebra

Golden rectangle

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.

Demonstration using geogebra

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.

Demonstration using geogebra

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

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,

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.

How to use excel to generate fibonnoci and golden ration

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)

GOLDEN SPIRAL

1/8 In golden ratio its closely packed.

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