mathematics

Michael Frame

Michael Frame is a mathematics 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 Michael Frame rather than just read about it. In short: Michael Frame is an American mathematician and retired Yale University professor. He is a co-author, along with Amelia Urry, of Fractal Worlds: Grown, Built, and Imagined.

Key takeaways

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

Reference excerpt

Michael Frame is an American mathematician and retired Yale University professor. He is a co-author, along with Amelia Urry, of Fractal Worlds: Grown, Built, and Imagined. At Yale, he was a colleague of Benoit Mandelbrot and helped Mandelbrot develop a curriculum within the mathematics department.

Early years and education Michael Frame was born in 1951 and grew up in St. Albans, West Virginia. After leaving his physics major because the lab requirement was "something in biophysics with killing frogs," Frame, a vegetarian, received a bachelor's degree in mathematics at Union College as a first-generation college student. In 1978, he completed a PhD in mathematics at Tulane University.

Teaching career Michael Frame came to work at Yale University at the invitation of his colleague Benoit Mandelbrot. At Yale, Frame called himself "the stupidest guy in the department...the dimmest bulb in the pack here," and focused on his teaching contributions. He received the McCredie Prize for best use of technology in teaching at Yale College, the Dylan Hixon '88 Prize for teaching excellence in the natural sciences, and the Yale Phi Beta Kappa chapter's DeVane medal for undergraduate teaching.

Work with Mandelbrot Benoit Mandelbrot includes a section on Michael Frame in his posthumously published autobiography The Fractalist: Memoir of a Scientific Maverick. In the section, called "Michael Frame, Friend and Colleague," he calls Frame an "indispensable" professor. In 1997, Mandelbrot and Frame held a meeting of teachers of fractal geometry. According to Mandelbrot, as far as he knew, this was the "first scientific meeting totally dedicated to the teaching of fractals. This eventually culminated in the 2002 publication of the book Fractals, Graphics, and Mathematics Education, which was co-authored by Frame and Mandelbrot.

References

Worked examples

Example 1 — a first encounter with Michael Frame

Start with the simplest possible case. Write down what Michael Frame claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Michael Frame 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 Michael Frame 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 Michael Frame

In research: Michael Frame appears in mathematics 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 Michael Frame 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: Michael Frame is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1951 births, American mathematicians, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Michael Frame 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 Michael Frame in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Michael Frame 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 Michael Frame out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Michael Frame in simple terms?

Michael Frame is an American mathematician and retired Yale University professor. He is a co-author, along with Amelia Urry, of Fractal Worlds: Grown, Built, and Imagined.

Why does Michael Frame matter?

Because it connects several mathematics 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 Michael Frame?

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 Michael Frame.