Établissement
Colegiul Ortodox "Mitropolitul Nicolae Colan" (Cluj-Roumanie)
Année
2023-2024
Résumé
Hugo Steinhaus (1887-1972), One Hundred Problems in Elementary Mathematics, 1963.
We write the two numbers 2 and 3: 23.
We take these two numbers, calculate their product 2 × 3 = 6 and write it down: 236.
We take the numbers 3 (again) and 6, calculate their product 3 × 6 = 18 and write it on the back: 23618.
We take the numbers 6 and 1, calculate their product 6 × 1 = 6 and write it as: 236186.
We repeat the process endlessly, this produces a series of numbers:
2361868484832323232246666666482436...
Is this sequence really infinite? What numbers appear in it? We notice blocks of consecutive identical numbers: 22, 6666666. Other numbers form do they have blocks like this? How many repetitions can there be? And if we change the starting numbers, what can happen?
We write the two numbers 2 and 3: 23.
We take these two numbers, calculate their product 2 × 3 = 6 and write it down: 236.
We take the numbers 3 (again) and 6, calculate their product 3 × 6 = 18 and write it on the back: 23618.
We take the numbers 6 and 1, calculate their product 6 × 1 = 6 and write it as: 236186.
We repeat the process endlessly, this produces a series of numbers:
2361868484832323232246666666482436...
Is this sequence really infinite? What numbers appear in it? We notice blocks of consecutive identical numbers: 22, 6666666. Other numbers form do they have blocks like this? How many repetitions can there be? And if we change the starting numbers, what can happen?
Ateliers qui présentent ce sujet
Type de présentation au congrès
Exposé
À présenter
aux lycéens
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