work done by teacher

1. 05/08/15 India's Contribution to Geometry 1
India’s
Contribution
to Geometry

2. Presented by
Mrs.Anita Deshmukh
SOS,Wanadongri, Nagpur
05/08/15 India's Contribution to Geometry 2
Constructions in Sulbasutra

3. What is sulbasutras ?What is sulbasutras ?
The beginning of Algebra can be traced
to the constructional Geometry of the
vedic priest which are preserved in the
sulabasutras .
Exact measurement , orientation and
different shapes for the altars and arenas
used for the religious functions are
described in sulbasutras.
05/08/15 India's Contribution to Geometry 3

4. To draw a square of which is equal toTo draw a square of which is equal to
the sum of areas of two unequal squaresthe sum of areas of two unequal squares
It is a construction based on Pythagoras theorem.
05/08/15 India's Contribution to Geometry 4
P Q
RS
X
Z
P Q
RS
A B
CD

5. ABCD and PQRS are the two given squares.
Mark a point X on PQ so that PX is equal to AB
Join SX
05/08/15 India's Contribution to Geometry 5
A B
CD
P Q
RS
X

6.  Draw a square on SX .
 Here , A(SXYZ) = SX2
, A (ABCD)= AB2
& A(PQRS ) =
PQ2
= SP2
 By Pythagoras theorem,
 PX2
+ SP2
= SX2
 AB2
+ SP2
= SX2
 A( ABCD ) + A ( PQRS ) = A ( SXYZ)□ □ □□ 05/08/15 India's Contribution to Geometry 6
Y
A B
CD
P Q
RS
X
Z

7. To draw a square equal to theTo draw a square equal to the
difference of two squaresdifference of two squares
05/08/15 India's Contribution to Geometry 7
A B
CD F
E
P
HK
Q
S
T
A B
CD
RS
Q P

8. Consider a square
ABCD
Take any point E on
AB .
Draw EF
perpendicular to AB
at E.
05/08/15 India's Contribution to Geometry 8
A B
CD F
E

9. With centre A and
radius AD draw an
arc to cut EF in P.
Join AP so that
AP = AD = AB
05/08/15 India's Contribution to Geometry 9
A B
CD F
E
P

10. Take a point H on EF such that AE = EH
Draw HK parallel to AE , so that AEHK is a
square.
05/08/15 India's Contribution to Geometry 10
A B
CD F
E
P
HK

11.  Draw PQ parallel to AE
 Choose a point on PQ
such that PE = PS
 Draw a perpendicular ST
on AB so that EPST is a square.
 Now , AP2
= AE2
+ EP2
 EP2
= AP2
- AE2
 A( EPST) = A( ABCD) – A( AEHK)□ □ □
05/08/15 India's Contribution to Geometry 11
A B
CD F
E
P
HK
Q
S
T

12. ReferencesReferences ::
Sarswati Amma
Prof. A.
Vyawhare
05/08/15 India's Contribution to Geometry 12

13. 05/08/15 India's Contribution to Geometry 13