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Mathematics Teaching in the Middle School, 2001
These questions address the relationship between area and perimeter and challenge children to think beyond rules that they may have been taught in school.
Bellasanta B. Ferrer +5 more
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These questions address the relationship between area and perimeter and challenge children to think beyond rules that they may have been taught in school.
Bellasanta B. Ferrer +5 more
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Packing Rectangles into the Unit Square
Geometriae Dedicata, 2000\textit{L. Moser} and \textit{J. W. Moon} [Colloq. Math. 17, 103-110 (1967; Zbl 0152.39502)] proved that every sequence of squares whose total area is not more than 1/2 can be packed (using isometries) into a unit square. Now Januszewski generalizes this to: a sequence of rectangles of side length at most 1 and total area at most 1/2 can be packed into
Janusz Januszewski
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Design of Optimized Reversible Squaring and Sum-of-Squares Units
Circuits, Systems, and Signal Processing, 2017Reversible logic has gained importance in the last few decades because of its low power dissipation. Quantum cost, garbage outputs, ancillary inputs and gate count are some of the performance parameters used to weigh reversible designs against one another. Optimization of these parameters is of great relevance to obtain an optimal design.
A. N. Nagamani +2 more
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Random dyadic tilings of the unit square
Random Structures & Algorithms, 2002AbstractA “dyadic rectangle” is a set of the formR= [a2−s, (a+ 1)2−s] × [b2−t, (b+ 1)2−t], wheresandtare nonnegative integers. A dyadic tiling is a tiling of the unit square with dyadic rectangles. In this paper we studyn‐tilings, which consist of 2nnonoverlapping dyadic rectangles, each of area 2−n, whose union is the unit square.
Svante Janson +2 more
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Combined multiplication and sum-of-squares units
Proceedings IEEE International Conference on Application-Specific Systems, Architectures, and Processors. ASAP 2003, 2004Multiplication and squaring are important operations in digital signal processing and multimedia applications. We present designs for units that implement either multiplication, A/spl times/B, or sum-of-squares computations, A/sup 2/+B/sup 2/, based on an input control signal.
Michael J. Schulte +4 more
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Comparing squaring and cubing units with multipliers
2012 IEEE 55th International Midwest Symposium on Circuits and Systems (MWSCAS), 2012With power becoming a precious resource in current VLSI systems, performance per Watt has become a more important metric than chip area. With a large number of applications benefitting from support for complex functional units like squaring and cubing, it becomes imperative that such functions be implemented in hardware.
Aditya M. Deshpande, Jeffrey Draper
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Discrete unit square cover problem
Discrete Mathematics, Algorithms and Applications, 2018In this paper, we consider the discrete unit square cover (DUSC) problem as follows: given a set [Formula: see text] of [Formula: see text] points and a set [Formula: see text] of [Formula: see text] axis-aligned unit squares in [Formula: see text], the objective is (i) to check whether the union of the squares in [Formula: see text] covers all the ...
Manjanna Basappa, Gautam K. Das
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Packing of non-blocking squares into the unit square
Colloquium MathematicumLet \(S_n\) be a square, for \(n = 1, 2,\dots\), and let \(I\) be a square of sidelength 1. We say that the squares \(S_1\), \(S_2\), \(\dots\) can be \textit{packed} into \(I\) if it is possible to apply translations and rotations to the sets \(S_n\) so that the resulting translated and rotated squares are contained in \(I\) and have mutually disjoint
Januszewski, Janusz, Zielonka, Łukasz
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A Note on Covering a Square of Side Length 2 + ∊ with Unit Squares
The American Mathematical Monthly, 2009(2009). A Note on Covering a Square of Side Length 2 + ∊ with Unit Squares. The American Mathematical Monthly: Vol. 116, No. 2, pp. 174-178.
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