MHB Show Metric Proves All Points Inside Circle Have Same Center

  • Thread starter Thread starter Julio1
  • Start date Start date
  • Tags Tags
    Geometric
AI Thread Summary
The discussion centers on proving that all points within a circle share the same center, using the metric $d_p(n+m)=|n-m|_p$. Participants clarify that the correct notation for the metric should be $d_p(m,n)=|n-m|_p$, which refers to the $p$-adic metric on the rational numbers. There is a request for a definition of a circle's center and clarification on the variable $p$. A link to a relevant resource is provided for further exploration of the topic. The conversation emphasizes the importance of precise definitions and notation in mathematical discussions.
Julio1
Messages
66
Reaction score
0
Show that all point inside of an circle is his center. Consider the metric $d_p(n+m)=|n-m|_p.$

Hello MHB :). Any hint for the problem?, thanks!.
 
Mathematics news on Phys.org
Hi, Julio.

Julio said:
Show that all point inside of an circle is his center. Consider the metric $d_p(n+m)=|n-m|_p.$
Could you give the definition of a circle center? Also, a metric is a function of two arguments, while $d_p(n+m)$ has one argument. Finally, what is $p$?
 
Julio said:
Show that all point inside of an circle is his center. Consider the metric $d_p(n+m)=|n-m|_p.$
I suppose you mean $d_p(m,n)=|n-m|_p$ where $d_p$ is the $p$-adic metric on $\mathbb{Q},$ and disc instead of circle. If so, have a look https://www.colby.edu/math/faculty/Faculty_files/hollydir/Holly01.pdf.
 
Last edited:
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
Back
Top