[4][1] Based on the success of Geometric Exercises in Paper Folding in Germany,[5] the Open Court Press of Chicago published it in the US, with updates by Wooster Woodruff Beman and David Eugene Smith.

[6] Later chapters of the book show how to construct algebraic curves including the conic sections, the conchoid, the cubical parabola, the witch of Agnesi,[7] the cissoid of Diocles,[8] and the Cassini ovals.

As well as Geometric Exercises in Paper Folding, he also wrote a second book, Elementary Solid Geometry, published in three parts from 1906 to 1909.

This was one of the Froebel gifts, a set of kindergarten activities designed in the early 19th century by Friedrich Fröbel.

First Lessons drew inspiration from Fröbel's gifts in setting exercises based on paper-folding, and from the book Elementary Geometry: Congruent Figures by Olaus Henrici in using a definition of geometric congruence based on matching shapes to each other and well-suited for folding-based geometry.

[10] In 1934, Margherita Piazzola Beloch began her research on axiomatizing the mathematics of paper-folding, a line of work that would eventually lead to the Huzita–Hatori axioms in the late 20th century.

Beloch was explicitly inspired by Rao's book, titling her first work in this area "Alcune applicazioni del metodo del ripiegamento della carta di Sundara Row" ["Several applications of the method of folding a paper of Sundara Row"].

[4] And in their own textbook on geometry using paper-folding exercises, The First Book of Geometry (1905), Grace Chisholm Young and William Henry Young heavily criticized Geometric Exercises in Paper Folding, writing that it is "too difficult for a child, and too infantile for a grown person".

[10] However, reviewing the 1966 Dover edition, mathematics educator Pamela Liebeck called it "remarkably relevant" to the discovery learning techniques for geometry instruction of the time,[7] and in 2016 computational origami expert Tetsuo Ida, introducing an attempt to formalize the mathematics of the book, wrote "After 123 years, the significance of the book remains.