science

Rectangular lattice

Rectangular lattice is a 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 Rectangular lattice rather than just read about it. In short: The rectangular lattice and centered rectangular lattice (or rhombic lattice) constitute two of the five two-dimensional Bravais lattice types. The symmetry categories of these lattices are wallpaper groups pmm and cmm respectively.

Key takeaways

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

Reference excerpt

The rectangular lattice and centered rectangular lattice (or rhombic lattice) constitute two of the five two-dimensional Bravais lattice types. The symmetry categories of these lattices are wallpaper groups pmm and cmm respectively. The conventional translation vectors of the rectangular lattices form an angle of 90° and are of unequal lengths.

Bravais lattices There are two rectangular Bravais lattices: primitive rectangular and centered rectangular (or rhombic).

The primitive rectangular lattice can also be described by a centered rhombic unit cell, while the centered rectangular lattice can also be described by a primitive rhombic unit cell. Note that the length a {\displaystyle a} in the lower row is not the same as in the upper row. For the first column above, a {\displaystyle a} of the second row equals a 2 + b 2 {\displaystyle {\sqrt {a^{2}+b^{2}}}} of the first row, and for the second column it equals 1 2 a 2 + b 2 {\displaystyle {\frac {1}{2}}{\sqrt {a^{2}+b^{2}}}} .

Crystal classes The rectangular lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the table below.

References

Illustrations

Worked examples

Example 1 — a first encounter with Rectangular lattice

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

In research: Rectangular lattice appears in 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 Rectangular lattice 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: Rectangular lattice is common in secondary-school and first-year university syllabi. It links to neighbouring topics Crystal systems, Crystallography stubs, Lattice points, so understanding it makes those chapters shorter.
In everyday life: Look for Rectangular lattice 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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Rectangular lattice in 20 minutes

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

Frequently asked questions

What is Rectangular lattice in simple terms?

Why does Rectangular lattice matter?

Because it connects several 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 Rectangular lattice?

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 Rectangular lattice.