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Pantriagonal magic cube

Pantriagonal magic cube 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 Pantriagonal magic cube rather than just read about it. In short: A pantriagonal magic cube is a magic cube where all 4m2 pantriagonals sum correctly. There are 4 one-segment pantriagonals, 12(m − 1) two-segment pantriagonals, and 4(m − 2)(m − 1) three-segment pantriagonals.

Key takeaways

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

Reference excerpt

A pantriagonal magic cube is a magic cube where all 4m2 pantriagonals sum correctly. There are 4 one-segment pantriagonals, 12(m − 1) two-segment pantriagonals, and 4(m − 2)(m − 1) three-segment pantriagonals. This class of magic cubes may contain some simple magic squares and/or pandiagonal magic squares, but not enough to satisfy any other classifications. The magic constant for magic cubes is S = m(m3 + 1)/2. A proper pantriagonal magic cube has 7m2 lines summing correctly. It contains no magic squares. The smallest pantriagonal magic cube has order 4. A pantriagonal magic cube is the 3-dimensional equivalent of the pandiagonal magic square – instead of the ability to move a line from one edge to the opposite edge of the square with it remaining magic, you can move a plane from one edge to the other.

See also Magic cube classes triagonal

References Heinz, H.D. and Hendricks, J. R., Magic Square Lexicon: Illustrated. Self-published, 2000, 0-9687985-0-0. Hendricks, John R., The Pan-4-agonal Magic Tesseract, The American Mathematical Monthly, Vol. 75, No. 4, April 1968, p. 384. Hendricks, John R., The Pan-3-agonal Magic Cube, Journal of Recreational Mathematics, 5:1, 1972, pp51-52. Hendricks, John R., The Pan-3-agonal Magic Cube of Order-5, JRM, 5:3, 1972, pp 205-206. Hendricks, John R., Pan-n-agonals in Hypercubes, JRM, 7:2, 1974, pp 95-96. Hendricks, John R., The Pan-3-agonal Magic Cube of Order-4, JRM, 13:4, 1980-81, pp 274-281. Hendricks, John R., Creating Pan-3-agonal Magic Cubes of Odd Order, JRM, 19:4, 1987, pp 280-285. Hendricks, J.R., Inlaid Magic Squares and Cubes 2nd Edition, 2000, 0-9684700-3-3. Clifford A. Pickover (2002). The Zen of Magic Squares, Circles and Stars. Princeton Univ. Press. 0-691-07041-5 page 178.

External links http://www.magichypercubes.com/Encyclopedia/ Aale de Winkel: Magic Encyclopedia http://members.shaw.ca/hdhcubes/cube_perfect.htm Harvey Heinz: Perfect Magic Hypercubes

Worked examples

Example 1 — a first encounter with Pantriagonal magic cube

Start with the simplest possible case. Write down what Pantriagonal magic cube 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 Pantriagonal magic cube 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 Pantriagonal magic cube 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 Pantriagonal magic cube

In research
Pantriagonal magic cube 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 Pantriagonal magic cube 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
Pantriagonal magic cube is common in secondary-school and first-year university syllabi. It links to neighbouring topics Magic squares, so understanding it makes those chapters shorter.
In everyday life
Look for Pantriagonal magic cube 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 Pantriagonal magic cube in 20 minutes

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

Frequently asked questions

What is Pantriagonal magic cube in simple terms?

A pantriagonal magic cube is a magic cube where all 4m2 pantriagonals sum correctly. There are 4 one-segment pantriagonals, 12(m − 1) two-segment pantriagonals, and 4(m − 2)(m − 1) three-segment pantriagonals.

Why does Pantriagonal magic cube 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 Pantriagonal magic cube?

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 Pantriagonal magic cube.

Tags

  • Magic squares

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