This video discusses lines in Euclidean geometry over finite fields, and shows why the Spread and Cross laws hold. The circumcenter and circumcircle of an example triangle are found over F_7.
Very true. The theory does not work in characteristic two, namely a field in which 2=0.
Let me also add that there is a further possible complication that happens in some fields---the denominator in the formula for spread can be zero, so the spread between two lines may be undefined. I will comment on this phenomenon, which relates to special relativity, in a later video.
Very true. The theory does not work in characteristic two, namely a field in which 2=0.
Let me also add that there is a further possible complication that happens in some fields---the denominator in the formula for spread can be zero, so the spread between two lines may be undefined. I will comment on this phenomenon, which relates to special relativity, in a later video.
njwildberger 3 years ago
1/4K, midpoints,... Seems that much of what you say excludes fields of characteristic two.
catalecticant 3 years ago