There is a popular story related to Apasthambha whose works on Kalpa and Griya Sutra texts are reference materials for experts in Vedic rituals.
Kalpa Sutras discuss the construction of Vedis 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 Vedis, 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 Apasthambha's texts which also list the steps in sqaring 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. They elaborate the details for smaller rituals meant for household use. Among these, the rituals related to anscestors contain the strictest rules. Apasthambha was an expert in these rules and was also a reformer.
Apasthambha was invited by a householder to a Shradha or the annual ritual for departed souls. The householder had been searching for the "perfect" guest to feed at the Shradha ceremony and Apasthambha sensed this as soon as her entered the house of the host. After feeding Apasthambha, the householder began offering Pindam or the ball of rice, to his anscestors. He took a cup of water to sprinkle water on the Pindam but the water would not leave his palm. Surprised, he looked at the face of Apasthambha.
Apasthambha said that anyone who regularly chants the Gayatri Mantra becomes eligible to be a guest to a Shradha 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 Apasthambha by this name after this incidence. There is a variation of this story in the Garuda Purana. Apasthambha uses the incidence to illustrate the importance of avoiding miserliness, anger and impatience during Sharadha ceremony.