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Julio1
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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!.
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.Julio said:Show that all point inside of an circle is his center. Consider the metric $d_p(n+m)=|n-m|_p.$
"Show Metric Proves All Points Inside Circle Have Same Center" is a mathematical concept that states that all points inside a circle have the same center. This means that no matter where you choose a point inside the circle, the distance from that point to the center will always be the same.
This metric is proven using the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. By applying this theorem to multiple points inside a circle, it can be proven that all points have the same distance to the center.
This metric is important because it is a fundamental property of circles and can be used to solve various problems in geometry and physics. It also helps to understand the relationship between the distance of points inside a circle and the circle's radius.
Yes, this metric applies to all circles, regardless of their size or location. As long as a point is inside the circle, it will have the same distance to the center as any other point inside the circle.
This metric has various real-world applications, such as in navigation, astronomy, and engineering. It helps in determining the distance between objects in circular motion, calculating the circumference and area of a circle, and finding the center of a circle. It is also used in creating precise measurements, such as in the construction of circular objects like wheels.