mathematics

Lee Sallows

Lee Sallows 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 Lee Sallows rather than just read about it. In short: Lee Cecil Fletcher Sallows (born April 30, 1944) is a British electronics engineer known for his contributions to recreational mathematics. He is particularly noted as the inventor of golygons, self-enumerating sentences, and geomagic squares.

Key takeaways

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

Reference excerpt

Lee Cecil Fletcher Sallows (born April 30, 1944) is a British electronics engineer known for his contributions to recreational mathematics. He is particularly noted as the inventor of golygons, self-enumerating sentences, and geomagic squares.

Recreational mathematics Sallows is an expert on the theory of magic squares and has invented several variations on them, including alphamagic squares and geomagic squares. The latter invention caught the attention of mathematician Peter Cameron, who has said that he believes that "an even deeper structure may lie hidden beyond geomagic squares". In "The lost theorem" published in 1997 he showed that every 3 × 3 magic square is associated with a unique parallelogram on the complex plane, a discovery that had escaped all previous researchers from ancient times down to the present day. A golygon is a polygon containing only right angles, such that adjacent sides exhibit consecutive integer lengths. Golygons were invented and named by Sallows and introduced by A.K. Dewdney in the Computer Recreations column of the July 1990 issue of Scientific American. In 2012 Sallows invented and named self-tiling tile sets—a new generalization of rep-tiles.

Triangle theorem

In 2014, Sallows discovered a previously unnoticed result, a way of using the medians to divide any triangle into three smaller triangles, all congruent with one another. Repeating the process on each triangle yields triangles similar to the original but a ninth the area.

Personal life Lee Sallows is the only son of Florence Eliza Fletcher and Leonard Gandy Sallows. He was born on 30 April 1944 at Brocket Hall in Hertfordshire, England, and grew up in the district of Upper Clapton in northeast London. Sallows attended Dame Alice Owen's School, then located at The Angel, Islington, but failed to settle in and was without diplomas when he left at age 17. Knowledge gained via interest in short-wave radio enabled him to find work as a technician within the electronics industry. In 1970, he moved to Nijmegen in the Netherlands, where, until 2009, he worked as an electronic engineer at Radboud University. In 1975, Sallows met his partner Evert Lamfers, a Dutch cardiologist, with whom he has lived ever since.

Bibliography 2014 Sallows, Lee "More On Self-tiling Tile Sets", Mathematics Magazine, April 2014 2012 Sallows, Lee. "On Self-Tiling Tile Sets", Mathematics Magazine, December, 2012 2012 "Geometric Magic Squares: A Challenging New Twist Using Colored Shapes Instead of Numbers", Dover Publications, ISBN 0486489094 1997 "The Lost Theorem", The Mathematical Intelligencer 1997 19; 4: 51–54. 1995 "The Impossible Problem", The Mathematical Intelligencer 1995 17; 1: 27–33. 1994 "Alphamagic Squares", In: The Lighter Side of Mathematics pp 305–39, Edited by R.K. Guy and R.E. Woodrow, pub. by The Mathematical Association of America, 1994, ISBN 0-88385-516-X 1992 Sallows, Lee (1992). "New pathways in serial isogons". The Mathematical Intelligencer. 14 (2): 55–67. doi:10.1007/BF03025216. S2CID 121493484. 1991 Sallows, Lee; Gardner, Martin; Guy, Richard K.; Knuth, Donald (1991). "Serial isogons of 90 degrees". Mathematics Magazine. 64 (5): 315–324. doi:10.2307/2690648. JSTOR 2690648. 1990 "A Curious New Result in Switching Theory", The Mathematical Intelligencer 1990; 12: 21–32. 1987 "In Quest of a Pangram", In: A Computer Science Reader, pp 200–20, Edited by EA Weiss, Springer-Verlag, New York, ISBN 978-1-4612-6458-3 1986 "Co-Descriptive Strings", (Lee Sallows & Victor L Eijkhout), Mathematical Gazette 1986; 70: 1–10

References

External links Official website

Illustrations

Worked examples

Example 1 — a first encounter with Lee Sallows

Start with the simplest possible case. Write down what Lee Sallows 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 Lee Sallows 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 Lee Sallows 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 Lee Sallows

In research: Lee Sallows 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 Lee Sallows 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: Lee Sallows is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1944 births, Combinatorial game theorists, LGBTQ mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Lee Sallows 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 Lee Sallows in 20 minutes

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

Frequently asked questions

What is Lee Sallows in simple terms?

Why does Lee Sallows 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 Lee Sallows?

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 Lee Sallows.