To receive a copy of the English workbook,
please contact Kathleen Pineau.
Divided into three parts, this activity will allow you to explore trigonometry and optimisation.
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You will become familiar with the various components of the apparatus through qualitati
ve exploration. You will then encode the relationships that exist between the different lengths by building formulas that use trigonometric functions. You will test the validity of your mathematical models, i.e. your formulas, by measuring the various lengths on the apparatus.
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Using your validated formulas, you will predict the equilibrium position of the weight for a new parameterization of the apparatus. You will do this in two ways: with graphs and with differential calculus. You will check how well you predicted the weight’s position by measuring it on the apparatus.
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Finally, you will refer back to your initial analysis and assess to what extent the final results reflect your initial impressions.
Historical Context
The Marquis Guillaume François Antoine de l'Hospital, count d'Autremont, marquis de Saint-Mesme (Paris 1661-1704, shown on the left) was one of Johann Bernoulli’s first students (Basel, Switzerland, 1667-1748, shown on the right).
In 1691, Bernoulli spent many months in Paris teaching the marquis the new math of the day, differential calculus. To illustrate the efficiency of this new field, Bernoulli presented him with the Weight problem that we will be working on.
The authors
France Caron, Université de Montréal, Alain Hénault et Kathleen Pineau, ÉTS.