mathematics

Alfred George Greenhill

Alfred George Greenhill 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 Alfred George Greenhill rather than just read about it. In short: Sir Alfred George Greenhill (29 November 1847 in London – 10 February 1927 in London), was a British mathematician. George Greenhill was educated at Christ's Hospital School and from there he went to St John's College, Cambridge in 1866.

Key takeaways

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

Reference excerpt

Sir Alfred George Greenhill (29 November 1847 in London – 10 February 1927 in London), was a British mathematician. George Greenhill was educated at Christ's Hospital School and from there he went to St John's College, Cambridge in 1866. In 1876, Greenhill was appointed professor of mathematics at the Royal Military Academy (RMA) at Woolwich, London, UK. He held this chair until his retirement in 1908, when he was knighted. His 1892 textbook on applications of elliptic functions is of acknowledged excellence. He was one of the world's leading experts on applications of elliptic integrals in electromagnetic theory. He was a Plenary Speaker of the ICM in 1904 at Heidelberg (where he also gave a section talk) and an Invited Speaker of the ICM in 1908 at Rome, in 1920 at Strasbourg, and in 1924 at Toronto.

Greenhill formula In 1879 Greenhill calculated complicated twist rate formulas for rifled artillery by approximating the projectile as an elongated ellipsoid of rotation in incompressible fluid (which, as he couldn't have known back then, assumes subsonic flight). Later, English ballistician F. W. Jones simplified it for typical bullet lengths into a rule of thumb for calculating the optimal twist rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowances for weight or nose shape. The eponymous Greenhill formula, still used today, is:

T w i s t = C D 2 L × S G 10.9 {\displaystyle \mathrm {Twist} ={\frac {CD^{2}}{L}}\times {\sqrt {\frac {SG}{10.9}}}}

where:

C = 150 (use 180 for muzzle velocities higher than 2,800 ft/s) D = bullet's diameter in inches L = bullet's length in inches SG = bullet's specific gravity (10.9 for lead-core bullets, which cancels out the second half of the equation) The original value of C was 150, which yields a twist rate in inches per turn, when given the diameter D and the length L of the bullet in inches. This works to velocities of about 840 m/s (2800 ft/s); above those velocities, a C of 180 should be used. For instance, with a velocity of 600 m/s (2000 ft/s), a diameter of 0.5 inches (13 mm) and a length of 1.5 inches (38 mm), the Greenhill formula would give a value of 25, which means 1 turn in 25 inches (640 mm). Recently, Greenhill formula has been supplemented with Miller twist rule.

Textbooks A. G. Greenhill Differential and integral calculus, with applications ( London, MacMillan, 1886) archive.org A. G. Greenhill, The applications of elliptic functions (MacMillan & Co, New York, 1892) University of Michigan Historical Mathematical Collection A. G. Greenhill, A treatise on hydrostatics (MacMillan, London, 1894) archive.org A. G. Greenhill, The dynamics of mechanical flight (Constable, London, 1912) archive.org A. G. Greenhill, Report on gyroscopic theory (Darling & Son, 1914)

References

External links

Quotations related to Alfred George Greenhill at Wikiquote Alfred George Greenhill. The First Century of the ICMI (1909 - 2008)

Worked examples

Example 1 — a first encounter with Alfred George Greenhill

Start with the simplest possible case. Write down what Alfred George Greenhill 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 Alfred George Greenhill 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 Alfred George Greenhill 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 Alfred George Greenhill

In research: Alfred George Greenhill 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 Alfred George Greenhill 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: Alfred George Greenhill is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1847 births, 1927 deaths, 19th-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Alfred George Greenhill 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 Alfred George Greenhill in 20 minutes

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

Frequently asked questions

What is Alfred George Greenhill in simple terms?

Why does Alfred George Greenhill 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 Alfred George Greenhill?

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 Alfred George Greenhill.