Definition:Lemniscate of Bernoulli/Geometric Definition/Mistake
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Source Work
1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables:
- Thème et variations
- $1,31102 87771 46059 90523 \ldots$
Mistake
- La lemniscate est l'ensemble des points $M$ du plan tels que le produit des distances à deux points fixes $P_1$, $P_2$ est $P_1 M \cdot P_2 M = C^{te} = \sqrt {P_1 P_2}$.
In English:
- The lemniscate is the set of points $M$ of the plane such that the product of the distances from two fixed points $P_1$, $P_2$ is $P_1 M \cdot P_2 M = C = \sqrt {P_1 P_2}$.
Correction
The constant is incorrect.
The expression ought to read:
- $P_1 M \cdot P_2 M = C = \paren {\dfrac {P_1 P_2} 2}^2$
That is,(when the half-distance between $P_1$ and $P_2$ is equal to the square root of the constant.
Sources
- 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,31102 87771 46059 90523 \ldots$