mathematics

Hendecagram

Hendecagram 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 Hendecagram rather than just read about it. In short: In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven vertices. The name hendecagram combines a Greek numeral prefix, hendeca-, with the Greek suffix -gram.

Key takeaways

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

Reference excerpt

In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven vertices. The name hendecagram combines a Greek numeral prefix, hendeca-, with the Greek suffix -gram. The hendeca- prefix derives from Greek ἕνδεκα (ἕν + δέκα, one + ten) meaning "eleven". The -gram suffix derives from γραμμῆς (grammēs) meaning a line.

Regular hendecagrams There are four regular hendecagrams, which can be described by the notation {11/2}, {11/3}, {11/4}, and {11/5}; in this notation, the number after the slash indicates the number of steps between pairs of points that are connected by edges. These same four forms can also be considered as stellations of a regular hendecagon. Since 11 is prime, all hendecagrams are star polygons and not compound figures.

Construction As with all odd regular polygons and star polygons whose orders are not products of distinct Fermat primes, the regular hendecagrams cannot be constructed with compass and straightedge. However, Hilton & Pedersen (1986) describe folding patterns for making the hendecagrams {11/3}, {11/4}, and {11/5} out of strips of paper.

Applications

Prisms over the hendecagrams {11/3} and {11/4} may be used to approximate the shape of DNA molecules.

Fort Wood, now the base of the Statue of Liberty in New York City, is a star fort in the form of an irregular 11-point star. The Topkapı Scroll contains images of an 11-pointed star Girih form used in Islamic art. The star in this scroll is not one of the regular forms of the hendecagram, but instead uses lines that connect the vertices of a hendecagon to nearly-opposite midpoints of the hendecagon's edges. 11-pointed star Girih patterns are also used on the exterior of the Momine Khatun Mausoleum; Eric Broug writes that its pattern "can be considered a high point in Islamic geometric design". An 11-point star-shaped cross-section was used in the Space Shuttle Solid Rocket Booster, for the core of the forward section of the rocket (the hollow space within which the fuel burns). This design provided more surface area and greater thrust in the earlier part of a launch, and a slower burn rate and reduced thrust after the points of the star were burned away, at approximately the same time as the rocket passed the sound barrier.

Illustrations

Worked examples

Example 1 — a first encounter with Hendecagram

Start with the simplest possible case. Write down what Hendecagram 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 Hendecagram 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 Hendecagram 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 Hendecagram

In research: Hendecagram 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 Hendecagram 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: Hendecagram is common in secondary-school and first-year university syllabi. It links to neighbouring topics 11 (number), Star polygons, so understanding it makes those chapters shorter.
In everyday life: Look for Hendecagram 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 Hendecagram in 20 minutes

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

Frequently asked questions

What is Hendecagram in simple terms?

In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven vertices. The name hendecagram combines a Greek numeral prefix, hendeca-, with the Greek suffix -gram.

Why does Hendecagram 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 Hendecagram?

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 Hendecagram.