Analysis of kd-tree, how is the vertical line L’s intersect areas equivalent to sqrt(N)?

I’m trying to understand how the number of intersected areas by a vertical line in a KD-tree is equivalent to sqrt(n)

If you draw a balanced KD-tree with 7 nodes.
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And then draw a vertical line l.

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The number of areas this line intersects should be equivalent to sqrt(N) where N is amount of nodes. (7)

When I count the areas the vertical line L intersects I get 5. But sqrt(7) = 2,6 not even close.

Both sources get to the recurrence:

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Which solves to O(sqrt(N)).

What am I doing wrong?


Source 1

Source 2