mathematics

Parallel parking problem

Parallel parking problem 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 Parallel parking problem rather than just read about it. In short: The parallel parking problem is a motion planning problem in control theory and mechanics to determine the path a car must take to parallel park into a parking space. The front wheels of a car are permitted to turn, but the rear wheels must stay aligned.

Key takeaways

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

Reference excerpt

The parallel parking problem is a motion planning problem in control theory and mechanics to determine the path a car must take to parallel park into a parking space. The front wheels of a car are permitted to turn, but the rear wheels must stay aligned. When a car is initially adjacent to a parking space, to move into the space it would need to move in a direction perpendicular to the allowed path of motion of the rear wheels. The admissible motions of the car in its configuration space are an example of a nonholonomic system.

See also Automatic parking Bicycle and motorcycle dynamics Falling cat problem Moving sofa problem

References Batterman, R (2003), "Falling cats, parallel parking, and polarized light" (PDF), Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 34 (4): 527–557, Bibcode:2003SHPMP..34..527B, doi:10.1016/s1355-2198(03)00062-5. Reeds, J.A.; Shepp, L.A. (1990), "Optimal paths for a car that goes both forwards and backwards" (PDF), Pacific Journal of Mathematics, 145 (2): 367–393, doi:10.2140/pjm.1990.145.367.

Illustrations

Parallel parking problem: Animation of a car parallel parking, turning only its front wheels — Animation of a car parallel parking, turning only its front wheels

Worked examples

Example 1 — a first encounter with Parallel parking problem

Start with the simplest possible case. Write down what Parallel parking problem 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 Parallel parking problem 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 Parallel parking problem 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 Parallel parking problem

In research: Parallel parking problem 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 Parallel parking problem 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: Parallel parking problem is common in secondary-school and first-year university syllabi. It links to neighbouring topics Applied mathematics stubs, Control theory, so understanding it makes those chapters shorter.
In everyday life: Look for Parallel parking problem 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 Parallel parking problem in 20 minutes

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

Frequently asked questions

What is Parallel parking problem in simple terms?

Why does Parallel parking problem 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 Parallel parking problem?

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 Parallel parking problem.