Pythagorean Approximation

Sum of one half of the shorter side and seven eighth of the longer side give the hypotenuse.

ஒடிய நீளன்தனை ஒரெட்டு கூரக்கி
கூரதில் ஒன்டை தள்ளி குன்ட்ரதின் பதியை சேர்தல்
நீடிய கருனம் தனே.

This poem says if you divide the run (the longer side) eight times and discard one portion and add that to the half of the height (the shorter side) what you get is the hypotenuse. This is a linear calculation without square root operation. For many architectural operations this can be done using ropes - without having to work with numbers.

The % error for most triangles that are not having angles close to 0/90 degree and 45 degree is very low. Due to the low error rate and the ease of use, this was used in many ancient engineering projects.

Examples:

This shortcut is known within Tamil department prior to 1980 at Sainik School, Amaravathinagar as a Tamil Poem (Sutra).