mathematics

Jules Hoüel

Jules Hoüel 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 Jules Hoüel rather than just read about it. In short: Guillaume-Jules Hoüel (7 April 1823 – 14 June 1886) was a French mathematician. He entered the École Normale Supérieure in 1843 and received his doctoral degree in 1855 from the Sorbonne.

Key takeaways

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

Reference excerpt

Guillaume-Jules Hoüel (7 April 1823 – 14 June 1886) was a French mathematician. He entered the École Normale Supérieure in 1843 and received his doctoral degree in 1855 from the Sorbonne. He was sought by Urbain Le Verrier at the Paris Observatory, but chose instead to return to Thaon to study there. In 1859 he began to teach at Bordeaux. In 1863 Hoüel expressed his doubts about the verifiability of the parallel postulate of Euclid. In 1867 Hoüel produced French translations of two key publications of non-Euclidean geometry: Lobachevski's Geometrical Studies on the Theory of Parallels and Bolyai's Science of Absolute Space. Hoüel published a four volume work titled Théorie Élémentaire des Quantités Complexes. Volume four, published in 1874, began with a discussion of properties of algebraic operations (commutativity, associativity, distribution, and inverses) and used the algebra of quaternions and versors to describe spherical trigonometry. However, in 1890 P. G. Tait revealed his dissatisfaction with Hoüel's changes in notation with text that Tait had given for Hoüel's use. Tait wrote:

The earliest offender in this class was the late M. Hoüel who, while availing himself of my permission to reproduce, in his Théorie Élémentaire des Quantités Complexes, large parts of this volume, made his pages absolutely repulsive by introducing fancied improvements in the notation. In 1876 Hoüel reviewed a Russian language quaternion textbook written by Romer (1868)

References

G. B. Halsted (1897) Guillaume-Jules Hoüel, American Mathematical Monthly 4:99–101, link from Jstor early content. O'Connor, John J.; Robertson, Edmund F., "Jules Hoüel", MacTutor History of Mathematics Archive, University of St Andrews Jules Hoüel in libraries (WorldCat catalog)

Illustrations

Worked examples

Example 1 — a first encounter with Jules Hoüel

Start with the simplest possible case. Write down what Jules Hoüel 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 Jules Hoüel 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 Jules Hoüel 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 Jules Hoüel

In research: Jules Hoüel 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 Jules Hoüel 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: Jules Hoüel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1823 births, 1886 deaths, 19th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jules Hoüel 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 “Jules Hoüel” →

Affiliate

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

How to study Jules Hoüel in 20 minutes

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

Frequently asked questions

What is Jules Hoüel in simple terms?

Guillaume-Jules Hoüel (7 April 1823 – 14 June 1886) was a French mathematician. He entered the École Normale Supérieure in 1843 and received his doctoral degree in 1855 from the Sorbonne.

Why does Jules Hoüel 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 Jules Hoüel?

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 Jules Hoüel.