computer science

Grapher

Grapher is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Grapher rather than just read about it. In short: Grapher is a computer program bundled with macOS since version 10.4 that is able to create 2D and 3D graphs from simple and complex equations. It includes a variety of samples ranging from differential equations to 3D-rendered Toroids and Lorenz attractors.

Key takeaways

Grapher belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Grapher to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Grapher from memory before moving on to harder problems.

Reference excerpt

Grapher is a computer program bundled with macOS since version 10.4 that is able to create 2D and 3D graphs from simple and complex equations. It includes a variety of samples ranging from differential equations to 3D-rendered Toroids and Lorenz attractors. It is also capable of dealing with functions and compositions of them. One can edit the appearance of graphs by changing line colors, adding patterns to rendered surfaces, adding comments, and changing the fonts and styles used to display them. Grapher is able to create animations of graphs by changing constants or rotating them in space.

History Before Grapher and Mac OS X, Mac OS 9 was bundled with Pacific Tech's Graphing Calculator, a similar program to Grapher that had been included with System 7. No versions of Mac OS X prior to Mac OS X v10.4 included a bundled graphing calculator application. On July 22, 2004, Apple bought Arizona Software's "Curvus Pro X," and renamed it “Graphing Calculator”, before deciding on “Grapher”. The news was publicly announced on September 15, 2004 at AppleInsider. Version 2.0 of Grapher was bundled with Mac OS X v10.5, and version 2.1 with Mac OS X v10.6. It was notable for being one of the few applications bundled with 10.6 to ship without 64-bit support. As of OS X 10.9, it became a 64-bit application.

Features Grapher is a graphing calculator capable of creating 2D graphs including classic (linear-linear), polar coordinates, linear-logarithmic, log-log, and polar log, as well as 3D graphs including standard system, cylindrical system, and spherical system. Grapher is a Cocoa application which takes advantage of Mac OS X APIs. It also supports multiple equations in one graph and exporting equations to LaTeX format, and comes with several pre-made equation examples. It is one of the few sophisticated graphing programs available capable of easily exporting clean vector art for use in printed documents, but exporting 3D graphs to vector is not possible. Animation of graphs is also supported in both 2D and 3D, generating a QuickTime file. It is also possible to use the operating system's copy-and-paste feature to copy equations from the application's visual equation editor. By doing so, Grapher functions as something of an equation editor; the user may copy images, EPS, PDF or LaTeX versions of entered equations into other applications. Any equation can be entered and copied; it is not limited to plottable equations.

References

External links Official user guide

Illustrations

Worked examples

Example 1 — a first encounter with Grapher

Start with the simplest possible case. Write down what Grapher claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Grapher before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Grapher ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Grapher

In research: Grapher appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Grapher in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Grapher is common in secondary-school and first-year university syllabi. It links to neighbouring topics MacOS-only software made by Apple Inc., Plotting software, TeX, so understanding it makes those chapters shorter.
In everyday life: Look for Grapher outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Grapher in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Grapher means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Grapher out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Grapher in simple terms?

Why does Grapher matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Grapher?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Grapher.