query: How can you show that each new line drawn on a plane creates another $k+1$ regions?
positive_passages.docid: 16582
positive_passages.text: Show that $n$ lines separate the plane into $\frac{n^2+n+2}{2}$ regions
negative_passages.docid: 150515
negative_passages.text: Construct an affine transformation of a plane given the images of three points
negative_passages.docid: 57897
negative_passages.text: Algorithm for computing the plane that passes through three arbitrary points
negative_passages.docid: 85650
negative_passages.text: Number or regions formed when $n$ points on a circle are joined
negative_passages.docid: 143717
negative_passages.text: Why/How are there infinite points in a line segment?
negative_passages.docid: 29713
negative_passages.text: $k$ times's draw from $n$ numbers with replacement, each number at least appear once
negative_passages.docid: 88184
negative_passages.text: Finding the value of $k$ for parallel/orthogonal planes
negative_passages.docid: 147429
negative_passages.text: Set of points in $\mathbb{C}$ s.t. $z^{n-1} = \overline z$
negative_passages.docid: 86815
negative_passages.text: Cutting a section from a sphere by planes
negative_passages.docid: 24477
negative_passages.text: Monochromatic squares in a colored plane
negative_passages.docid: 5667
negative_passages.text: Marking points of intersection between two curves
negative_passages.docid: 129002
negative_passages.text: Number of triangles formed by $m$ lines
negative_passages.docid: 141482
negative_passages.text: Proof that plane with $N$ lines can be painted with two colors so that any two neighboring regions are painted in different colors
negative_passages.docid: 150522
negative_passages.text: Do circles divide the plane into more regions than lines?
negative_passages.docid: 116538
negative_passages.text: Proof of Connected Diagrams
negative_passages.docid: 105459
negative_passages.text: Creating lots of random cuts on a surface
negative_passages.docid: 146045
negative_passages.text: Generating stippled (Penrose-style) drawings of surfaces