Use of irrational numbers for coordinate system

In summary, the preference for using an irrational coordinate system over a rational one depends on the type of graph being plotted and the convenience of using different units of measure. Some graphs, such as sine waves, may be more easily plotted on an irrational coordinate system, while others may be more easily plotted on a rational one. Ultimately, the choice of coordinate system depends on the purpose and context of the graph.
  • #1
Faiq
348
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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.
 
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  • #2
Faiq said:
the coordinate axis on most of the graphs always irrational
Is this true?
 
  • #3
DrClaude said:
Is this true?
Edited
 
  • #4
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
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
Faiq said:
By irrational grid system I mean a grid in which π,eπ,eπ,e can be plotted.
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
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.
 
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  • #8
Faiq said:
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.
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.
 

Related to Use of irrational numbers for coordinate system

What are irrational numbers?

Irrational numbers are numbers that cannot be expressed as a ratio of two integers. They are non-terminating and non-repeating decimals. Examples of irrational numbers include pi (3.141592...) and the square root of 2 (1.414213...).

Why are irrational numbers used in coordinate systems?

Irrational numbers are used in coordinate systems because they allow for more precise and accurate measurements. Rational numbers, which are limited to whole numbers and fractions, can only approximate the location of a point on a graph. Irrational numbers provide a more precise and continuous representation of the coordinate system.

How are irrational numbers represented in coordinate systems?

Irrational numbers are represented as points on a number line in coordinate systems. The decimal representation of an irrational number can be used to determine its location on the number line. For example, the irrational number pi would be represented as a point between 3 and 4 on the number line.

What are the advantages of using irrational numbers in coordinate systems?

The use of irrational numbers in coordinate systems allows for more accurate and precise measurements. This is particularly important in fields such as science, engineering, and mathematics where precise measurements are necessary for calculations and analyses. Additionally, irrational numbers allow for a continuous representation of the coordinate system, which is important for graphing and visualizing data.

Are there any limitations to using irrational numbers in coordinate systems?

One limitation of using irrational numbers in coordinate systems is that they cannot be easily expressed as fractions or whole numbers. This can make calculations and conversions more complex. Additionally, some computer programs and calculators may have difficulty accurately representing or manipulating irrational numbers.

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