🇦🇺𝕄𝕦𝕟𝕥𝕖𝕕𝕔𝕣𝕠𝕔𝕠𝕕𝕚𝕝𝕖@lemm.ee to Science Memes@mander.xyzEnglish · 8 months agoFuck geometrylemm.eeimagemessage-square50linkfedilinkarrow-up1290arrow-down112
arrow-up1278arrow-down1imageFuck geometrylemm.ee🇦🇺𝕄𝕦𝕟𝕥𝕖𝕕𝕔𝕣𝕠𝕔𝕠𝕕𝕚𝕝𝕖@lemm.ee to Science Memes@mander.xyzEnglish · 8 months agomessage-square50linkfedilink
minus-squareOrganicMustard@lemmy.worldlinkfedilinkEnglisharrow-up3·8 months agoYou can make something like this properly by defining a different metric. For example with metric dl2 = dx2 - dy2 the vector (1, 1) has length 0, so you can make a “triangle” with sides of lengths 1, -1 and 0.
minus-squareKogasa@programming.devlinkfedilinkEnglisharrow-up2·8 months agoThat’s not a metric. In any metric, distances are positive between distinct points and 0 between equal points
minus-squaretechnocrit@lemmy.dbzer0.comlinkfedilinkEnglisharrow-up1arrow-down1·8 months agoThis is true for real-valued metrics but not complex-valued metrics. https://en.wikipedia.org/wiki/Complex_measure
minus-squareKogasa@programming.devlinkfedilinkEnglisharrow-up2·8 months agoMetric, not measure. Metrics are real by definition.
You can make something like this properly by defining a different metric. For example with metric dl2 = dx2 - dy2 the vector (1, 1) has length 0, so you can make a “triangle” with sides of lengths 1, -1 and 0.
That’s not a metric. In any metric, distances are positive between distinct points and 0 between equal points
This is true for real-valued metrics but not complex-valued metrics.
https://en.wikipedia.org/wiki/Complex_measure
Metric, not measure. Metrics are real by definition.