astronomy

Magic hexagram

Magic hexagram is a astronomy 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 Magic hexagram rather than just read about it. In short: A magic hexagram of order 2 is an arrangement of numbers in a hexagram with triangular cells with 2 cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant M. Magic star hexagram Magic star hexagram or 6-pointed magic star is a star polygon with Schläfli symbol {6/2} in which numbers are placed at each of the six vertices and six intersections, such tha…

Key takeaways

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

Reference excerpt

A magic hexagram of order 2 is an arrangement of numbers in a hexagram with triangular cells with 2 cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant M.

Magic star hexagram

Magic star hexagram or 6-pointed magic star is a star polygon with Schläfli symbol {6/2} in which numbers are placed at each of the six vertices and six intersections, such that the four numbers on each line sum to the same magic constant.

Magic star hexagram with triangular cell

There are two solutions of magic star hexagram with 12 triangular cells.

Magic star hexagram with more than 12 vertices

Harold Reiter and David Ritchie calculated the solution of magic hexagrams with 19 vertices.

Illustrations

Worked examples

Example 1 — a first encounter with Magic hexagram

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

In research: Magic hexagram appears in astronomy 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 Magic hexagram 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: Magic hexagram is common in secondary-school and first-year university syllabi. It links to neighbouring topics Magic figures, Star symbols, so understanding it makes those chapters shorter.
In everyday life: Look for Magic hexagram 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 Magic hexagram in 20 minutes

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

Frequently asked questions

What is Magic hexagram in simple terms?

Why does Magic hexagram matter?

Because it connects several astronomy 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 Magic hexagram?

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 Magic hexagram.