There is a popular story related to Apastamba whose works on Kalpa and Grihya Sutra texts are reference materials for experts in Vedic rituals. Kalpa Sutras discuss the construction of a Vedi or the central fire pit for Yagnas. Strict rules dictate the geometry of a Vedi, right down to the size of individual bricks. Different shaped Vedi, namely, circular, semi-circular, square, rectangular, must occupy the same sized area. Mathematicians have found estimates to the square root of the number two to ten digital places in Apastamba’s texts which also list the steps in squaring a circle and dividing a circle into seven equal parts. Mathematicians wonder about the fact that these were known centuries before the start of the Common Era.
Grihya Sutra texts are the domestic counter parts of Kalpa Sutras. People who know only the Griya Sutras do not recognize the mathematician Apastamba. They elaborate the details for smaller rituals meant for household use. Among these, the rituals related to ancestors contain the strictest rules. Apastamba was an expert in these rules and was also a reformer.
Apastamba was invited by a householder to a Shraddha or the annual ritual for departed souls. The householder had been searching for the “perfect” guest to feed at the Shraddha ceremony and Apastamba sensed this as soon as her entered the house of the host. After feeding Apastamba, the householder began offering Pindam or the ball of rice, to his ancestors. He took a cup of water to sprinkle water on the Pindam or Pinda but the water would not leave his palm. Surprised, he looked at the face of Apastamba.
Apastamba said that anyone who regularly chants the Gayatri Mantra becomes eligible to be a guest to a Shraddha ceremony. He explained that great scholarship is not a compulsory criteria for a guest. The name Apa-Sthambha refers to one who can stop the flow of water. People started calling Apastamba by this name after this incidence. There is a variation of this story in the Garuda Purana. Apastamba uses the incidence to illustrate the importance of avoiding miserliness, anger and impatience during Sharadha ceremony.