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MAC OS X GRAPHER DOWNLOAD

9/18/2018

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Grapher is one of those tools on OS X that is sadly abandoned. Getting Started
With Grapher, Your Mac's Built-in Graph Tool. Unlimited Downloads.

Successful puttering in mathematics requires some way of visualizing the
equations you are playing with. It’s all very well to slap around some equation
using just a pencil and paper, but there’s a lot of information to be gained
from actually looking at the beast.

So a good graphing program is an essential part of the putterer’s toolkit. Mac
OS X users are blessed with a built-in graphing program called Grapher. It’s
easy to use, surprisingly powerful, and best of all, free. Its one weakness lies
in its documentation – you’ve got to wade through pages of help and sample files
in order to figure out what it can and can’t do. For people who are already
intimidated by mathematics, this can prove to be an insurmountable obstacle.

Therefore I thought my first series of blog entries would be a basic user’s
guide to Grapher. Starting Grapher Go to the Applications folder -> Utilities ->
Grapher.app. Start it up, and you will be rewarded with this window (click on
image to expand). A blank worksheet Grapher’s worksheet has three panes: the
equation editor on the top, where you will enter your equation; the equation
list on the left, which keeps track of the different equations that are being
displayed; and the graph area itself. Entering Equations Entering equations is
very intuitive with Grapher – just type them into the equation editor much as
you would write them on paper.

Division is handled with the “/” key, exponentiation with the “^” key.
Multiplication uses the “*” key, although you can often leave it out, e.g., 5x
instead of 5*x. Regular order of operations applies.

There are, however, a few quirks to keep in mind. When you have finished typing
in an exponent, you have to hit the right arrow key in order to signal to
Grapher that the exponent is finished. Otherwise any subsequent typing will be
considered as part of the exponent.

The same principle applies to denominators – when finished with the denominator,
hit the right arrow key to let Grapher know that the rest of the equation is not
part of the denominator. If you type in a parenthesis, Grapher will
automatically insert a pair of parentheses, with the expectation that you will
start typing your expression in the middle. This is useful for keeping track of
nested parentheses, but is sometimes confusing for those of us who are used to
entering parentheses one at a time.

By the way, Grapher does not recognize square brackets when nesting parentheses
– so restrain yourself and just use the rounded ones. More complicated
expressions can be entered with the help of the Equation Palette. This will be
covered in subsequent blog posts. Explicit Equations Explicit equations have the
form y = f(x), where the y is all by itself on the left hand side of the “=”,
and there is some function of x on the right. For example: y=x^2/(1-x). If you
type in that equation and hit enter, Grapher immediately draws a plot and enters
the new equation into the equation list. Zoomed-out plot of y = x^2/(1-x)
showing second branch Sure enough, a second branch of the equation appears.

Note that the axes of the plot were automatically adjusted. To further explore
our plot, we can use the Point Probe. Simply click on a portion of the curve
that is of interest, and crosshairs will appear, with the x and y coordinates of
the crosshairs displayed at the bottom of the screen. Note that the Point Probe
always “locks on” to the nearest curve. In this plot, I would like to see where
the maximum of the second branch is. Point Probe showing local maximum around
(2,-4) This is very useful for estimating the zeros of functions, or the
locations of local minima/maxima. Implicit Equations Grapher handles implicit
equations (i.e., those where the x’s and y’s are mixed together) with equal
aplomb.

To add a new equation to the existing worksheet, you can go to the menu and
choose Equation -> New Equation, or you can hit Command-Option-N. Then type an
implicit equation into the equation editor, e.g., x^2/4+y^2/1 = 1. The astute
putterer will recognize this as the equation of a 2×1 ellipse, and Grapher
confirms.

Plot of x^2/4 + y^2/1 = 1 6. Multiple Equations/Selecting Note that there are
now two equations in the Equation List. If you click on the ellipse equation, it
gets selected and the other function is greyed out; if you click on the first
equation, it gets selected and the ellipse gets greyed out. If you get tired of
looking at a particular equation, you can uncheck the check box to its left, and
its graph will temporarily disappear. Polar equations While Grapher has polar
graph paper, you can plot polar equations equally well on the default axes. In
fact, you can plot them simultaneously with rectangular equations. Just remember
to use “r” and “θ” instead of “y” and “x”, and Grapher will immediately
understand that this equation is in polar coordinates.


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