Quantum redactiones paginae "Circulus" differant
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inserted interioris: the circle itself has no area (being a one-dimensional set of points) |
amplificatio stipulae |
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Linea 15:
:: <math>A = \pi \cdot r^2.</math>
==Aequatio circuli==
Linea circuli cum centro <math> M(u|v) </math> radioque <math> r </math> exprimitur per formulam:
:: <math> (x - u)^2 + (y - v)^2 = r^2 </math>
Hoc ita demonstrari potest:
Per definitionem circuli omnia puncta in linea circuli sita ab centro aequidistantia sunt: <math> \overline{MX} = r </math>. Haec aequatio ita transformatur:
<math> \overline{MX} = r </math>,
ergo <math> |\overrightarrow{MX}| = r </math>,
ergo <math> |\vec x - \vec m| = r </math>,
ergo <math> |\begin{pmatrix} x - u \\ y - v \end{pmatrix}| = r </math>,
ergo <math> \sqrt{(x - u)^2 + (y - v)^2} = r </math>,
ergo <math> (x - u)^2 + (y - v)^2 = r^2 </math>, q. e. d.
{{math-stipula}}
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