mathematics

John Casey (mathematician)

John Casey (mathematician) 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 John Casey (mathematician) rather than just read about it. In short: John Casey (12 May 1820, Kilbehenny, County Limerick, Ireland – 3 January 1891, Dublin) was a respected Irish geometer. He is most famous for Casey's theorem on a circle that is tangent to four other circles, an extension of Ptolemy's theorem.

Key takeaways

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

Reference excerpt

John Casey (12 May 1820, Kilbehenny, County Limerick, Ireland – 3 January 1891, Dublin) was a respected Irish geometer. He is most famous for Casey's theorem on a circle that is tangent to four other circles, an extension of Ptolemy's theorem. However, he contributed several novel proofs and perspectives on Euclidean geometry. He and Émile Lemoine are considered to be the co-founders of the modern geometry of the circle and the triangle.

Biography He was born at Kilbehenny in Limerick, Ireland and educated locally at Mitchelstown, before becoming a teacher under the Board of National Education. He later became headmaster of the Central Model Schools in Kilkenny City. He subsequently entered Trinity College Dublin in 1858, where he was elected a Scholar in 1861 and was awarded the degree of BA in 1862. He was then Mathematics Master at Kingston School (1862–1873), Professor of Higher Mathematics and Mathematical Physics at the newly founded Catholic University of Ireland (1873–1881) and Lecturer in Mathematics at its successor, the University College Dublin (1881–1891).

Honours and awards In 1869, the University of Dublin awarded Casey the Honorary Degree of Doctor of Laws. He was elected a Fellow of the Royal Society in June 1875. He was elected to the Royal Irish Academy and in 1880 became a member of its council. In 1878 the Academy conferred upon him the much coveted Cunningham Gold Medal. His work was also acknowledged by the Norwegian Government, among others. He was elected a member of the Societe Mathematique de France in 1884 and received the honorary degree of Doctor of Laws from the Royal University of Ireland in 1885.

Major works 1880: On Cubic Transformations 1881: On Cyclides and Sphero-quartics, from Internet Archive 1882: The First Six Books of the Elements of Euclid, link from Project Gutenberg 1885: A Treatise on the Analytic Geometry of the Point, Line, Circle and Conic Sections, Second edition, 1893, links from Internet Archive 1886 A Sequel to the First Six Books of Euclid, 4th edition, link from Internet Archive 1886: A Treatise on Elementary Trigonometry (Dublin, 1886) 1888: A Treatise on Plane Trigonometry containing an account of the Hyperbolic Functions 1889: A Treatise on Spherical Geometry, link from Internet Archive

References

Sources Irish Monthly (1891), XIX, 106, 152 Proc. Royal Society (1891), XLIX, 30, p. xxiv.

Further reading Carlyle, Edward Irving (1901). "Casey, John" . In Lee, Sidney (ed.). Dictionary of National Biography (1st supplement). London: Smith, Elder & Co. 1913 Catholic Encyclopedia article on John Casey "James Maher, Chief of the Comeraghs, Mullinahone, 1957, pp 295–299.

External links Works by John Casey at Project Gutenberg Works by or about John Casey at the Internet Archive

Illustrations

Worked examples

Example 1 — a first encounter with John Casey (mathematician)

Start with the simplest possible case. Write down what John Casey (mathematician) 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 John Casey (mathematician) 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 John Casey (mathematician) 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 John Casey (mathematician)

In research: John Casey (mathematician) 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 John Casey (mathematician) 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: John Casey (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1820 births, 1891 deaths, 19th-century Irish mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for John Casey (mathematician) 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “John Casey (mathematician)” →

Affiliate

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

How to study John Casey (mathematician) in 20 minutes

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

Frequently asked questions

What is John Casey (mathematician) in simple terms?

Why does John Casey (mathematician) 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 John Casey (mathematician)?

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 John Casey (mathematician).