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Tag Archives: silver
The curious powers of 1 + sqrt 2: recurrences
In my previous post, we found an answer to the question: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? However, the solution depended on having the clever idea to add . … Continue reading
Posted in number theory, puzzles
Tagged conjecture, digits, powers, puzzle, ratio, silver
8 Comments
The curious powers of 1 + sqrt 2: a clever solution
Recall that we are trying to answer the question: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? In my previous post, we computed for some small and conjectured that the answer … Continue reading
Posted in number theory, puzzles
Tagged conjecture, digits, powers, puzzle, ratio, silver
2 Comments
The curious powers of 1 + sqrt 2: conjecture
In my previous post I related the following puzzle from Colin Wright: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? Let’s play around with this a bit and see if we … Continue reading
Posted in number theory, puzzles
Tagged conjecture, digits, powers, puzzle, ratio, silver
3 Comments
The curious powers of 1 + sqrt 2
Recently on mathstodon.xyz, Colin Wright posted the following puzzle: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? Of course, it’s simple enough to use a computer to find the answer; any … Continue reading