diff --git a/src/geometry/manhattan-distance.md b/src/geometry/manhattan-distance.md index 87514868a..86e1d0485 100644 --- a/src/geometry/manhattan-distance.md +++ b/src/geometry/manhattan-distance.md @@ -67,11 +67,11 @@ To prove this, we just need to analyze the signs of $m$ and $n$. And it's left a We may apply this equation to the Manhattan distance formula to find out that -$$d((x_1, y_1), (x_2, y_2)) = |x_1 - x_2| + |y_1 - y_2| = \text{max}(|(x_1 + y_1) - (x_2 + y_2)|, |(x_1 - y_1) - (x_2 - y_2)|).$$ +$$d((x_1, y_1), (x_2, y_2)) = |x_1 - x_2| + |y_1 - y_2| = \text{max}(|(x_1 + y_1) - (x_2 + y_2)|, |(y_1 - x_1) - (y_2 - x_2)|).$$ -The last expression in the previous equation is the [Chebyshev distance](https://en.wikipedia.org/wiki/Chebyshev_distance) of the points $(x_1 + y_1, x_1 - y_1)$ and $(x_2 + y_2, x_2 - y_2)$. This means that, after applying the transformation +The last expression in the previous equation is the [Chebyshev distance](https://en.wikipedia.org/wiki/Chebyshev_distance) of the points $(x_1 + y_1, y_1 - x_1)$ and $(x_2 + y_2, y_2 - x_2)$. This means that, after applying the transformation -$$\alpha : (x, y) \to (x + y, x - y),$$ +$$\alpha : (x, y) \to (x + y, y - x),$$ the Manhattan distance between the points $p$ and $q$ turns into the Chebyshev distance between $\alpha(p)$ and $\alpha(q)$. pFad - Phonifier reborn

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