Parabolas, Lines and Nomograms
Before the invention of the calculator, people always sought methods or tools to perform calculations easily, such as the abacus, which dates back to ancient times (21st century BC), or the slide rule in more recent times (17th century AD).
The nomogram, a simple example of which is shown below, is a graphical calculation tool instead.
A nomogram generally consists of three scales (in our case, the two branches of the parabola and the y-axis): the line segment connecting two points on the outer scales intercepts the result of the operation the tool was designed for on the third scale.
Can you figure out what the nomogram in the app is used for?
A Question...
Do you think that if we used points on the parabola with rational x-coordinates instead of integer ones, we would still get the expected result of the operation? Explain the reason for your answer.