An Easy But Impossible Probability Problem
I like looking a little deeper into problems; here we’ll find that although the problem is simple if you take it on its own terms, those terms are actually impossible. Does it matter?
Month: June 2025
Internal and External Division of a Segment
Last time, we considered how to represent algebraically the division of a line segment in a given ratio. At the end, we touched on a subject I recalled discussing extensively almost four years ago: that such a “division” can be either internal (inside the segment, as you’d expect) or external (elsewhere on the line containing …
Dividing a Segment: Get the Order Right!
A series of recent questions dealt with proportional division of a line segment. The context was vectors, and we’ll use them a lot, though the main ideas can be understood using ordinary geometry. We’ll see a mistake so easy to make that AI did it just as humans do; and how textbooks can make it …