There is an ancient poem in Tamil
which tells you how to calculate Hypotenuse
for a triangle
. The time period in which the poem was written is unknown, but it surely provides an (approximate) alternative to Pythogoras
Here the poem is (in Unicode Tamil):
ஓடிய நீளந்தன்னை ஓரெட்டு கூறதாக்கி கூற்றிலே ஒன்று தள்ளி
குன்றத்தில் பாதி சேர்த்தால் வருவது கர்ணம் தானே.
Poem in Romanized Tamil:
Odiya n-ILan-thannai Orettu kURathAkki kURRilE onRu thaLLi
kunRaththil pAthi sErththAl varuvathu karNam thAnE.
Divide the distance you've run (longer side) into 8 equal parts and discard one part from it. Then if you add the half the height to that, you'll get Hypotenuse.
Take a Right angled triangle with sides 3 and 4 units
Now as per the poem, Hypotenuse = (7/8)*4 + 3/2 = 5.
example 2, take a Right angled triangle with sides 3 and 6
Hypotenuse = (7/8)*6 + 3/2 = 6.75
By the actual pythagorian theorem, Hypotenuse = SQRT(6^2 + 3^2) = 6.71