التفاصيل البيبلوغرافية
| العنوان: |
PERFECT PACKING OF SQUARES. |
| المؤلفون: |
JOÓS, ANTAL |
| المصدر: |
Mathematical Reports; 2023, Vol. 25 Issue 2, p221-229, 9p |
| مصطلحات موضوعية: |
GENERALIZATION, MATHEMATICAL bounds, MATHEMATICAL notation, INTEGERS, MATHEMATICAL proofs |
| مستخلص: |
It is known that ∞ΣPi=1 1/i² = π²/6. Meir and Moser asked what is the smallest ϵ such that all the squares of sides of length 1, 1/2, 1/3, . . . can be packed into a rectangle of area π²/6 + ϵ. A packing into a rectangle of the right area is called perfect packing. Chalcraft packed the squares of sides of length 1, 2-t, 3-t, . . . and he found perfect packing for 1/2 < t ≤ 3/5. We will show, based on an algorithm by Chalcraft, that there are perfect packings if 1/2 < t ≤ 2/3. Moreover, we show that there is a perfect packing for all t in the range log3 2 ≤ t ≤ 2/3. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
Complementary Index |
