I Use of irrational numbers for coordinate system

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1. Sep 12, 2017

Faiq

Why should a person prefer irrational coordinate system over rational?

My friend stated that its because most lines such as $y=e$ cannot be plotted on a rational grid system. But that cannot be true since $e$ does have a rational number summation $2+1/10+7/100...$ which can be utilised to plot $y=e$ on the rational coordinate system.

So why don't we use rational number coordinate system?

P.S. By irrational grid system I mean a grid in which $π,e$ can be plotted.

Last edited: Sep 12, 2017
2. Sep 12, 2017

Staff: Mentor

Is this true?

3. Sep 12, 2017

Faiq

Edited

4. Sep 12, 2017

Staff: Mentor

It depends on what you plot. For instance, if you have a sine waves, it makes sense to use tick marks at multiples of some fraction of π, especially if plotting by hand.

On a computer, everything is easy to calculate, but one might still use irrational ticks for purposes of visualization.

I don't remember ever seeing an axis in terms of e.

5. Sep 12, 2017

Staff: Mentor

We do use logarithmic plotting and polar plotting which are different from a linear scale.

In order to be adopted by other folks, you'd need to suggest a use for the rational plotting case and perhaps provide an example.

Just to ask why isn't always helpful but it is inventive and this is sometimes how new math is developed.

6. Sep 12, 2017

jbriggs444

That is, you imagine a sheet of graph paper where the grid lines are laid out at in a somewhat irregular pattern such as at $\sqrt{2}$, $e$, $\pi$, $e \pi$ and integer multiples thereof?

Nothing stops one from plotting $y= e^x$ on ordinary ruled paper. Though one can use semi-log ruled paper instead.

https://www.printablepaper.net/category/log

7. Sep 12, 2017

FactChecker

What is irrational in one unit of measure is rational in another. A right angle can be irrational (1.5707963267949 radians), radians expressed in rational units of π, integer (90°), or rational (1/4 rotation). Most people would use the most convenient units for their work. In the context of trig functions, I imagine that some people would label the axes in rotations, but I think that most people label the axis either in rational units of π or in radians. You can Google "sine graph" and see images with all various axis labels. On the other hand, if you Google "graph", you will see images whose axes are predominately integers.

Last edited: Sep 12, 2017
8. Sep 12, 2017

Staff: Mentor

Although the terms in the series are all fractions (and thus rational), the sum of the series is an irrational number -- e.
Although we can locate the exact position of the number e on the real number line, we can approximate its location to just about any desired precision.