Difference between revisions of "Simple ratio"
From Encyclopedia of Mathematics
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| − | ''of three points | + | ''of three points $M_1,M,M_2$ on a straight line'' |
| − | The number | + | The number $\lambda$ such that |
| − | + | $$\overline{M_1M}=\lambda\overline{MM_2}$$ | |
| − | One says, moreover, that | + | One says, moreover, that $M$ divides the segment $M_1M_2$ in the ratio $\lambda$. If $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of $M_1$ and $M_2$, then the coordinates of $M$ are |
| − | + | $$x=\frac{x_1+\lambda x_2}{1+\lambda},\quad y=\frac{y_1+\lambda y_2}{1+\lambda}.$$ | |
The simple ratio is an invariant of affine transformations. | The simple ratio is an invariant of affine transformations. | ||
Latest revision as of 09:24, 13 April 2014
of three points $M_1,M,M_2$ on a straight line
The number $\lambda$ such that
$$\overline{M_1M}=\lambda\overline{MM_2}$$
One says, moreover, that $M$ divides the segment $M_1M_2$ in the ratio $\lambda$. If $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of $M_1$ and $M_2$, then the coordinates of $M$ are
$$x=\frac{x_1+\lambda x_2}{1+\lambda},\quad y=\frac{y_1+\lambda y_2}{1+\lambda}.$$
The simple ratio is an invariant of affine transformations.
How to Cite This Entry:
Simple ratio. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Simple_ratio&oldid=12601
Simple ratio. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Simple_ratio&oldid=12601
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article