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Episode 60 – The Cartesian Coordinate System (Graphing)

In this episode I talk about a way of mapping out points on a grid of squares.  This mapping method is called the Cartesian coordinate system and it a very common method to create graphs..   Way back there in Episode 1, I talked about taking measurements and we used a ruler to take those measurements.  A ruler is marked with whole numbers with marks indicating where these points are on the ruler.  A Cartesian coordinate system has two of these with the two of these at 90 degrees in relation to each other.  90 degrees was chosen to prevent the two values from interacting with each other.

Usually the horizontal line starting at zero is called the X-axis, and they vertical line is called the Y-axis.  When data is charted on this type of graph, the X-axis data is called the “independent variable”, and the Y-axis data is called the “dependant variable”.  This is because the X-axis variable is adjusted by whoever is presenting the data, and the Y-axis variable is affected by that adjustment.  (Please note the word “usually” – It is not always the case.)   When the values of the data for individual points is shown on the graph it is normally shown in the form “(X-value,Y-value)”. For example the point where the two axes cross each other is at point (0,0) and is given the special name of “the origin” of the graph.

So far I have talked about a graph where all of the points are greater than zero (positive) on both axes.  Sometimes, the data is negative on one or both axes.  For example, in the winter time, temperature often gets “below zero” or negative. If we assume the graph is drawn with 4 equal sized “windows” each of these areas is called a quadrant as shown in the 2nd picture.  Data often can be in all four quadrants.

Sometimes, it is useful to present concepts just showing the quadrants only.  Kind of a semi-joke is the 3rd picture which shows what I call “the knowledge matrix”.   in the first quadrant is the area we are happy to be in, the place where we know what we know.  The third quadrant is where life is really bad. For example, we have disassembled our automobile, and have discovered we don’t know how to put it back together.

Graphs can be generated by taking actual data and then allowing the data to develop understanding of the device or process we are studying.   Also, graphs can be generated by using mathematics and formulas to create the data.   Hopefully, the formulas, are an accurate representation of reality so the pretty graphs are telling us something factual.  (In many cases, there are some questions about models and formulas attempting to predict the future.)

There is some extra detail about all of this in the audio, I have pretty much only presented an outline of this subject in this written version.  This will all be put to use in the next episode which will be about the ellipsograph and trying to understand it well enough to create a model of how it works.

Should you decide to comment on this post, please include something in your statement to indicate that you have read the post, or that you have listened to the audio.  I have been getting a lot of spam, and I am having to delete almost all comments that do not show some indication they are real comments and not just a chance for someone to get their site linked on a web site.

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Thank you for your time.

Gary

 

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