New horizons
Non-Euclidean geometry, projective geometry: each new vision extends the concept of line. The notion of 'the shortest path from one point to another' gives a glimpse of the notion of geodesic on a surface, with surprises and fun problems. And computers get involved to help us construct lines!
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Straight lines in curved spaces: geodesics
If we restrict ourselves to a surface, the shortest path from one point to another is called a geodesic. This concept leads "straight" to non-Euclidean geometries and applications in navigation and cartography.
The projective line: a fruitful new perspective
The line is the simplest geometric figure imaginable. The variety of situations encountered in geometry may seem more complicated, and yet… might there be a special perspective from which the plane could be understood as a line? That is precisely what projective geometry is about!
Drawing a line on a computer
What could be simpler than drawing a line between two points? All you need is a ruler and a pencil! But how do you do it on a computer screen? How does graphics software manage it? The task is to turn certain points on the screen black. But which ones?