Corpus ID: 119163861

Pi Visits Manhattan

@article{RudolphLilith2017PiVM,
  title={Pi Visits Manhattan},
  author={M. Rudolph-Lilith},
  journal={arXiv: History and Overview},
  year={2017}
}
Is it possible to draw a circle in Manhattan, using only its discrete network of streets and boulevards? In this study, we will explore the construction and properties of circular paths on an integer lattice, a discrete space where the distance between two points is not governed by the familiar Euclidean metric, but the Manhattan or taxicab distance, a metric linear in its coordinates. In order to achieve consistency with the continuous ideal, we need to abandon Euclid's very original… Expand

Figures and Tables from this paper

On a Recursive Construction of Circular Paths and the Search for $$\pi $$π on the Integer Lattice $$\mathbb {Z}^2$$Z2
TLDR
A new algorithm for the construction of digital circles on the integer lattice Z2, which makes sole use of the signum function, which recovers the defining constantπ of a circle in R2, in a space endowed withℓ1-norm. Expand

References

SHOWING 1-10 OF 23 REFERENCES
On a Recursive Construction of Circular Paths and the Search for $$\pi $$π on the Integer Lattice $$\mathbb {Z}^2$$Z2
TLDR
A new algorithm for the construction of digital circles on the integer lattice Z2, which makes sole use of the signum function, which recovers the defining constantπ of a circle in R2, in a space endowed withℓ1-norm. Expand
The Story of the Binomial Theorem
1. The early period. The Binomial Theorem, familiar at least in its elementary aspects to every student of algebra, has a long and reasonably plain history. Most people associate it vaguely in theirExpand
A chronological and mathematical overview of digital circle generation algorithms – introducing efficient 4- and 8-connected circles
TLDR
A 4- and an 8-connected all integer algorithm, which proceed without any multiplication, using just one addition per iteration to compute the decision variable, which makes them more efficient than previously published algorithms. Expand
Area, Lattice Points, and Exponential Sums
Introduction Part I Elementary Methods 1. The rational line 2. Polygons and area 3. Integer points close to a curve 4. Rational points close to a curve Part II The Bombieri-Iwaniec Method 5. AnalyticExpand
Digital geometry - geometric methods for digital picture analysis
TLDR
Curves and Surfaces: Topology, 3D Straightness and Planarity, and Surface and Area Curvature. Expand
Introduction to analytic number theory
This is the first volume of a two-volume textbook which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. It provides an introductionExpand
Combinatorial Methods with Computer Applications
  • J. Gross
  • Mathematics, Computer Science
  • 2007
TLDR
Objectives of Combinatorics Ordering and Selection Some Rules of Counting Counting Selections Permutations Graphs Number-Theoretic Operations Combinatorial Designs. Expand
Gesammelte Abhandlungen
  • Nature
  • 1906
THE first volume of Prof. Abbe's works has already been noticed in the pages of NATURE (vol. lxix., p. 497). The contents of the second volume, while extremely interesting, are more miscellaneous inExpand
A linear algorithm for incremental digital display of circular arcs
TLDR
Methodology for producing dot or step patterns closest to the true circle, which can be drawn on an incremental display device such as a cathode ray tube, digital plotter, or matrix printer. Expand
...
1
2
3
...