### 3.2 Descartes and the Coordinate Graph

This lesson leads off with an intro to Rene Descartes the 17th century philosopher who is credited with coming up with the idea of coordinate geometry (not surprisingly called the Cartesian coordinate system.) There's a cool, but most likely apocryphal story of how Descartes discovered the idea. My quick Google search came with this description:

Note: You can find an interesting introduction to this topic at “Descartes and the Fly.”

If you are a bit hazy about how coordinates work, I would suggest that before you tackle the Set I problems you try this fun way to introduce (or review) exploring the X-Y plane with Billy the bug!

Set II questions 1 to 6 start to make the connection between ordered pairs and functions. (We will return to this idea in lesson 3.)

Set III (editions 1 and 2 only) is a bit tedious (and dated?) but my students loved doing it! (Spoiler: see attached file on the Jacobs site.) Set III in edition 3 is more textbookish.

How did you make out?

One morning [], Descartes found himself watching a fly on the wall (or so the story goes) and suddenly discovered that he could define the fly’s position using only three numbers: the perpendicular distance of the fly from each wall and from the ceiling. Generalizing from this realization, he discovered that any point in space could be defined in a similar way by measuring their distances from perpendicular lines or planes. These numbers have commonly become known as “Cartesian coordinates” and the perpendicular lines as the x- and y-axes. That discovery led to the development of analytical geometry, the first mathematical blending of algebra and geometry. The discovery of the coordinate plane, alone, is a huge contribution to psychology, for without it, defining the relationship between independent and dependent variables, calculating correlations, performing tests of significance, and other quantitative analysis would not be possible. (Snipped from this site.)

Note: You can find an interesting introduction to this topic at “Descartes and the Fly.”

If you are a bit hazy about how coordinates work, I would suggest that before you tackle the Set I problems you try this fun way to introduce (or review) exploring the X-Y plane with Billy the bug!

Set II questions 1 to 6 start to make the connection between ordered pairs and functions. (We will return to this idea in lesson 3.)

Set III (editions 1 and 2 only) is a bit tedious (and dated?) but my students loved doing it! (Spoiler: see attached file on the Jacobs site.) Set III in edition 3 is more textbookish.

How did you make out?

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