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05/08/15 India's Contribution to Geometry 1
India’s
Contribution
to Geometry
Presented by
Mrs.Anita Deshmukh
SOS,Wanadongri, Nagpur
05/08/15 India's Contribution to Geometry 2
Constructions in Sulbasutra
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
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
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
 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
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
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
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
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
 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
ReferencesReferences ::
Sarswati Amma
Prof. A.
Vyawhare
05/08/15 India's Contribution to Geometry 12
05/08/15 India's Contribution to Geometry 13

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Paper presentation anita_mam[1]

  • 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