India’s contribution to geometry[1]

INDIA’S CONTRIBUTION TO GEOMETRY

AT BHIDE GIRLS’ HIGH SCHOOL, NAGPUR

1ST & 2ND DECEMBER, 2012

CONSTRUCTION OF ISOSCELES TRAPEZIUM

Presented by- Rishi Agrawal,

Head, Dept. of Mathematics, Hislop College, Nagpur.

Tithi Agrawal, Grade – 7,

Edify School, Nagpur.

TRAPEZIUM (TRAPEZOID)

I have only one set of parallel sides.

My median is parallel to the bases and equal to one-half

the sum of the bases.

Isosceles TrapezoidI have:- only one set of parallel sides- base angles congruent- legs congruent- diagonals congruent- opposite angles supplementary

ISOSCELES TRAPEZOID

ISOSCELES TRAPEZIUM IN DAILY LIFE

Baudhāyana, (fl. c. 800 BCE) was an Indian mathematician, who was most likely also a priest. He is noted as the author of the earliest Sulba Sūtra—appendices to the Vedas giving rules for the construction of altars—called the Baudhāyana Śulbasûtra, which contained several important mathematical results.

He is older than the other famous mathematician Āpastambha. He belongs to the Yajurveda school.

He is accredited with calculating the value of pi before pythagoras, and with discovering what is now known as the Pythagorean theorem.

Baudhayana made the following constructions :

1)To draw a straight line at right angles to a given straight line.

2)To draw a straight line at right angles to a given straight line to a given point from it .

3)To construct a square having a given side. 4)To construct a rectangle of given sides. 5)To construct a isosceles trapezium of a given

altitude, face and base.

6)To construct a parallelogram having given sides at a given inclination.

7)To draw a square equivalent to n times a given square.

8)To draw a square equivalent to the sum of two different squares.

9)To draw a square equivalent to two given triangles.

10)To transform a rectangle into square.

11)To transform a square into rectangle.12)To transform a square into an rectangle

which shall have an given side . 13)To transform a square or a rectangle into an

triangle . 14)To transform a square into an rhombus. 15)To transform a rhombus into an square.

DRAWING ISOSCELES TRAPEZIUM

• Draw two parallel line segments of equal length, say AB and CD.• Take P as midpoint of CD.• Join PA and PB.• Draw PM as altitude of ΔPAB.

• Consider a point Q on MP produced. • With the center at M and radius MQ, draw an

arc of a circle, cutting line CD at points E and F. • Join AE and BF. • AEFB is an isosceles trapezium.

DRAWING ISOSCELES TRAPEZIUM

DRAWING ISOSCELES TRAPEZIUM

Proof : Δ APM and BPM are congruent.Also ME = MF = radius of circle.Therefore, Δ MEP are MFP are congruent.=> Δ AEP and BFP are congruent.=> AE = BFTherefore, trapezium is isosceles with two non

parallel equal sides.

Thank U!!!