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1 year ago in History of Mathematics , Mathematical Analysis By Farheen Ahmed

What are some methods to solve Archimedes’ square root of 3 problem?

As someone working through historical mathematical problems, I’m fascinated by Archimedes’ geometric and numerical techniques. I’m looking for actionable steps or algorithms that can be implemented, not just the historical context, to understand the computational thinking of the era.

HistoryOfMathematics SquareRoot

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By Riya N Answered 1 year ago

I've often revisited this problem when teaching the history of numerical analysis. I would recommend starting with the classic geometric approach using an iterative bounding technique between fractions, which Archimedes himself might have employed. For a more algebraic path, consider applying the Babylonian method, or Heron's method, as it's sometimes known, to the equation x² = 3. This iterative process converges quickly and offers a clear, practical computational experience that mirrors later developments. The key is to compare the efficiency and rationale behind each historical step.

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