“In fact, we typically use ‘rational’ to refer to something more reason-based or similar,” Kolaczyk says. “Its use in mathematics seems to have arisen as early as the year 1200 in British sources (according to the Oxford English Dictionary). If you trace both ‘rational’ and ‘ratio’ back to their Latin roots, you will find that in both cases the root has to do with with ‘reasoning’, in general terms”.
What is clearer is that both rational and irrational numbers have played an important role in the advancement of civilization.
While language probably dates back to roughly the origin of the human species, numbers appeared much later, explains Marcos Zegarelli, math tutor and author who has written 10 books in the “For Dummies” series. Hunter-gatherers, he says, probably didn’t need much numerical precision, other than the ability to roughly estimate and compare quantities.
“They needed concepts like ‘We don’t have any more apples,'” Zegarelli says. “They didn’t need to know, ‘We have exactly 152 apples.'”
But as humans began to till plots of land to create farms, build cities, and manufacture and trade goods, moving further and further from their homes, they needed more complex mathematics.
“Suppose you build a house with a roof whose elevation is the same length as the span from the base to its highest point,” Kolaczyk says. “How long is the extent of the roof surface from the top to the outside edge? It is always a factor of the square root of 2 of the elevation (stroke). And that is also an irrational number.”