Professional paper

$p$-norms on $\R^2$, $S_p$ circles and $\pi_p$ numbers

Ljiljana Arambašić ; PMF-Matematički odjel, Zagreb, Hrvatska
Ivona Zavišić ; {Nadbiskupska klasična gimnazija, Zagreb, Hrvatska

Abstract

The ratio of the circumference of a circle to its diameter is constant and its value is the number $\pi=3.14159...$. Here we understand that the circumference and the diameter are calculated with respect to the usual euclidean metric. Instead, we can equip $\R^2$ with some other metric. Choosing the metric $d_p,$ induced by the $p$-norm, the ratio of the circumference to the diameter will also be constant, but its value will be changed. In this paper we discuss $p$-norms and metrics $d_p$, the circles $S_p$ and the numbers $\pi_p$ with respect to these norms.

Keywords

$p$-norms on $\R^2$; $S_p$ circles and $\pi_p$ numbers

Hrčak ID:

66970

URI

https://hrcak.srce.hr/66970

Publication date:

19.4.2011.

Article data in other languages: croatian

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