2:45 My native language is Brazilian Portuguese, but I've been studying and using English as my primary language for about 10 years now. As for my nickname, it's actually a funny story that happened by chance!
7:00 I used algorithms to create sets of five special dice that have six sides, numbered from 1 to 30, with numbers that are evenly distributed on each die and add up to 93. When you roll these dice against each other, the chances of one die rolling higher than the other two is about 55.5% (20/36 probability). The idea behind these special dice is similar to 'Rock-Paper-Scissors-Spock-Lizard'. I was hoping to use these dice sets as a tool for role-playing games or similar projects. Here is an example: Given the following 6-sided dice (and their sides as a list) - Die A {1,2,21,22,23,24}, Die B {3,4,16,17,26,27}, Die C {5,6,8,15,29,30}, Die D {7,10,11,18,19,28}, Die E{ 9,12,13,14,20,25} -, the probability that one die rolls higher ("beats") than other two is 20/36: A beats D and E; B beats A and E; C beats A and B; D beats B and C; E beats C and D. 😉
By the way, you can search for "Cut the Knot Non-Transitive Dice" (without quotes) on Google. You'll find a detailed PDF explanation that goes beyond what I've shared here.
54:30 The Liouville surface seems to be related to the torus, which is also connected to the Hopf fibration. I'm wondering if the Liouville surface can be thought of as a type of Hopf fibration or something entirely different.
2:45 My native language is Brazilian Portuguese, but I've been studying and using English as my primary language for about 10 years now. As for my nickname, it's actually a funny story that happened by chance!
7:00 I used algorithms to create sets of five special dice that have six sides, numbered from 1 to 30, with numbers that are evenly distributed on each die and add up to 93. When you roll these dice against each other, the chances of one die rolling higher than the other two is about 55.5% (20/36 probability). The idea behind these special dice is similar to 'Rock-Paper-Scissors-Spock-Lizard'. I was hoping to use these dice sets as a tool for role-playing games or similar projects. Here is an example:
Given the following 6-sided dice (and their sides as a list) - Die A {1,2,21,22,23,24}, Die B {3,4,16,17,26,27}, Die C {5,6,8,15,29,30}, Die D {7,10,11,18,19,28}, Die E{ 9,12,13,14,20,25} -, the probability that one die rolls higher ("beats") than other two is 20/36: A beats D and E; B beats A and E; C beats A and B; D beats B and C; E beats C and D. 😉
By the way, you can search for "Cut the Knot Non-Transitive Dice" (without quotes) on Google. You'll find a detailed PDF explanation that goes beyond what I've shared here.
54:30 The Liouville surface seems to be related to the torus, which is also connected to the Hopf fibration. I'm wondering if the Liouville surface can be thought of as a type of Hopf fibration or something entirely different.