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Results tagged with euclidean-geometry
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user 3816
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these.
6
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1
answer
472
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Algorithm to decide whether two constructible numbers are equal?
The set of constructible numbers
https://en.wikipedia.org/wiki/Constructible_number
is the smallest field extension of $\mathbb{Q}$ that is closed under square root and complex conjugation. I am lo …
- 1,282
2
votes
2
answers
251
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Procedure to determine the equality of numbers in rationals plus square root
Consider the set $\mathbb{Q}^\sqrt{}$ of real numbers that can be constructed by applying finitely many of the five operations $+$, $-$, $\cdot$, $/$ and $\sqrt{}$ to a positive rational number. Examp …
- 1,282
3
votes
1
answer
357
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Equality of Euclidean numbers / constructible numbers
Euclidean numbers are those real number that can be constructed from the natural numbers by a finite chain of +,-,*,/ and $\sqrt{}$. They are also called Constructible Numbers.
I am now interested in …
- 1,282
2
votes
1
answer
122
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Proving coincidence in Euclidean geometry by using finitely many constellations
Two polynomials $f(x)$ and $g(x)$ of degree $n$ are equal if they are equal for $n+1$ different $x$.
Is anything like this true for Euclidean geometry? Say, I have three arbitrary points in the plan …
- 1,282