The 3,4,5 probably came from a technique for building structures that have 90 degree angles. — frank
" /| Alice's elapsed time = / | Bob's elapsed time? 1 year / | √(1^2 - 0.6^2) = / | 0.8 years (9.6 months) ------ Bob's travel distance = 0.6 light years (in Alice's reference frame) "
But which came first: the idea or the visualization? — frank
That this subject [imaginary numbers] has hitherto been surrounded by mysterious obscurity, is to be attributed largely to an ill adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question. — Carl Friedrich Gauss
Unfortunately, the link has been taken down. But as an Architect, I'm familiar with the "practical trick", as Frank called it. For those interested in the pre-Pythagorean history of the theorem, Howard Bloom goes into extravagant detail on how the pragmatic rule-of-thumb was used long before anyone developed a theory to explain it mathematically, or to interpret its magic spiritually, or to build a mathematics cult upon its foundation.But which came first: the idea or the visualization? — frank
Wow! So an idea can interfere with visualization? Change your ideas and new doors open for visualization? — frank
Thought you'd like this — frank
How is 3,4,5 divine? — frank
Could you guys share your philosophy of math with me? — frank
That's actually a beautiful picture of things. I think it leads to a problem of evil though. Do you have a solution? — frank
Could you guys share your philosophy of math with me? — frank
Our developed human intellectual abilities add two things to those simple perceptions. The first is visualisation, which allows us to understand necessary relations between mathematical facts. Try this easy mental exercise: imagine six crosses arranged in two rows of three crosses each, one row directly above the other. I can equally imagine the same six crosses as three columns of two each. Therefore 2 × 3 = 3 × 2. I not only notice that 2 × 3 is in fact equal to 3 × 2, I understand why 2 × 3 must equal 3 × 2. — The mathematical world - James Franklin
imagine six crosses arranged in two rows of three crosses each, one row directly above the other. I can equally imagine the same six crosses as three columns of two each. Therefore 2 × 3 = 3 × 2. I not only notice that 2 × 3 is in fact equal to 3 × 2, I understand why 2 × 3 must equal 3 × 2. — The mathematical world - James Franklin
Probably came from algebra x2 + y2 = z2
32 + 42 = 52 — EnPassant
ptolemy's theorem — talminator2856791
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