• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Hyper-volume by integration Xorter Fellow Posts: 91 Threads: 30 Joined: Aug 2016 04/08/2017, 01:52 PM (This post was last modified: 04/08/2017, 05:15 PM by Xorter. Edit Reason: spelling ) Hi, everyone! My dream is to get a formula to get the n-dimensional hyper-volume of an n-dimensional function in cartesian AND polar coordinates, too! So the length of f(x), the area of f(x,y), the volume of f(x,y,z) ... etc. According to the other existing formulas I have created an own in cartesian coordinate system: $V_N = \int ... \int_{V_N} \sqrt{1+\sum_{k=1}^N {}{df \over dx_k}} dx_1 ... dx_N$ 1st question: Do you find it correct? 2nd: How could it look in polar coordinate system? (My final goal is to use these formulas to determine a few things about the base units of the hyperdimensional and interdimensional spaces from its derivatives and its existences. But for it, I need these formulas!) Xorter Unizo « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Thoughts on hyper-operations of rational but non-integer orders? VSO 2 930 09/09/2019, 10:38 PM Last Post: tommy1729 Hyper operators in computability theory JmsNxn 5 4,734 02/15/2017, 10:07 PM Last Post: MphLee Recursive formula generating bounded hyper-operators JmsNxn 0 1,720 01/17/2017, 05:10 AM Last Post: JmsNxn holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 17,899 08/22/2016, 12:19 AM Last Post: JmsNxn on constructing hyper operations for bases > eta JmsNxn 1 3,015 04/08/2015, 09:18 PM Last Post: marraco Bounded Analytic Hyper operators JmsNxn 25 22,465 04/01/2015, 06:09 PM Last Post: MphLee Integration? 73939 11 15,263 09/10/2014, 08:46 PM Last Post: tommy1729 Integration of x^x Ryan 2 3,435 02/25/2014, 08:28 AM Last Post: Gottfried Incredible reduction for Hyper operators JmsNxn 0 2,460 02/13/2014, 06:20 PM Last Post: JmsNxn Hyper operator space JmsNxn 0 2,075 08/12/2013, 10:17 PM Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)