Hervé Lehning
90 articles published in Tangente
Math for everyoneN°187Mar 25, 2019Envelopes, moving points and evolutes
The envelope of a family of lines can be understood in two ways. The second lends itself better to computation, but both give rise to superb geometric questions.
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Math for everyoneN°186Jan 22, 2019The Pythagorean theorem: an elegant proof
Leonardo da Vinci was not strictly speaking a mathematician, but the subject interested him, as it did many educated men of the Renaissance. We owe him an elegant proof of the Pythagorean theorem.
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History and CultureN°69Jan 17, 2019Newton's fluxions
With his theory of fluxions, Newton explained Kepler's laws describing planetary motion. Yet because it was less convenient to use than Leibniz's infinitesimal calculus, it ultimately held back research in Britain.
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Math for everyoneN°185Nov 21, 2018Pre-Columbian numeral systems
In which we discover that South American civilizations did not wait for Christopher Columbus before adopting numeral systems
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Math for everyoneN°68Oct 10, 2018Misuse and security
While AI makes large-scale data collection and analysis easier, it also enables greater surveillance of the population. Every coin has two sides...
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History and CultureN°68Oct 10, 2018Computer-assisted proofs
Can a machine prove a theorem? Probably not without a human to guide it, but computers are becoming increasingly useful assistants—for example, by turning a human proof into a formal one. Spectacular developments and applications are currently under way.
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History and CultureN°67Jun 29, 2018Antarctica, a continent still shrouded in mystery…
Unlike in the Arctic, where the area covered by winter sea ice is shrinking, Antarctica's ice-covered area is growing. How can this paradox be explained when temperatures are rising?
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Math for everyoneN°67Jun 29, 2018The predator–prey system
Without predators, an animal population grows exponentially, ultimately sealing its fate. Predation can establish a balance… but may also lead to the species' extinction or to chaotic situations!
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Math for everyoneN°67Jun 28, 2018Sustainable development: an oxymoron?
An oxymoron is a figure of speech that brings together two seemingly contradictory terms. Thus, in Le Cid (1637), Corneille coined the phrase “that dark radiance falling from the stars”
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History and CultureN°182May 17, 2018From breaking the ADFGVX cipher to victory
For the second phase of the German spring offensives of 1918, the Germans added the letter V to the ADFGX cipher. But Georges Painvin broke the new cipher within hours… paving the way for final victory. The new system, though apparently more sophisticated, was actually weaker!
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History and CultureN°182May 17, 2018Locating enemy artillery
During the Great War, artillery caused two-thirds of all casualties. Locating enemy batteries was therefore important so that counter-battery fire could silence them. Surprisingly, the search leads to an old geometry problem!
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Math for everyoneN°181Mar 18, 2018Interpreting statistical data correctly
Big Data's vast resources are exploited using algorithms based on statistics and probability. This explains both the successes and failures of this technology.
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