Related Experiment Video
Updated: Jul 18, 2026

Experiments on Ultrasonic Lubrication Using a Piezoelectrically-assisted Tribometer and Optical Profilometer
Published on: September 28, 2015
The number of N-point digital discs
Martin N Huxley1, Jovisa Zunić
1School of Mathematics, Cardiff University, Cardiff, UK. Huxley@cf.ac.uk
Abstract:
A digital disc is the set of all integer points inside some given disc. Let {\cal D}_{N} be the number of different digital discs consisting of N points (different up to translation). The upper bound D(N) = O(N(2)) was shown recently; no corresponding lower bound is known. In this paper, we refine the upper bound to D(N) = O(N), which seems to be the true order of magnitude, and we show that the average [formula: see text] has upper and lower bounds which are of polynomial growth in N.
Related Concept Videos
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule
Degrees of Freedom
For example, suppose there are three unknown numbers whose mean is 10; although we can freely assign values to the first and second numbers, the value of the last number can not be arbitrarily assigned.
Degrees of Freedom
For example, suppose there are three unknown numbers whose mean is 10; although we can freely assign values to the first and second numbers, the value of the last number can not be arbitrarily...
Degenerative Disc Disease ll: Pathophysiology
Rules for Significant Figures
It should be emphasized that when we represent measured values, the...
Center of Mass: Introduction

