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BP569 |
| Triangular number of dots vs. non-triangular number of dots |
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COMMENTS
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All examples in this Problem are groups of black dots.
The nth triangular number is the sum over the natural numbers from 1 to n, where n > 0. Note: 0 is the 0th triangular number. The first few triangular numbers are 0, 1, 3 (= 1+2) and 6 (= 1+2+3) |
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CROSSREFS
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Adjacent-numbered pages:
BP564 BP565 BP566 BP567 BP568  *  BP570 BP571 BP572 BP573 BP574
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KEYWORD
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nice, precise, allsorted, notso, number, math, left-narrow, left-null, help, preciseworld
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WORLD
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dots [smaller | same | bigger]
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AUTHOR
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Leo Crabbe
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BP564 |
| Discrete points intersecting boundary of convex hull vs. connected segment intersecting boundary of convex hull |
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COMMENTS
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If a "string" is wound tightly around the shape, does one of its segments lie directly on the shape?
All examples in this Problem are connected line segments or curves.
We are taking lines here to be infinitely thin, so that if the boundary of the convex hull intersects the endpoint of a line exactly it is understood that they meet at 1 point. |
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CROSSREFS
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Adjacent-numbered pages:
BP559 BP560 BP561 BP562 BP563  *  BP565 BP566 BP567 BP568 BP569
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EXAMPLE
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Imagine wrapping a string around the pointed star. This string would take the shape of the boundary of the star's convex hull (a regular pentagon), and would only touch the star at the end of each of its 5 individual tips, therefore the star belongs on the left. |
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KEYWORD
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hard, nice, allsorted, solved, perfect
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AUTHOR
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Leo Crabbe
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BP562 |
| There exists a closed trail that hits each vertex exactly once vs. not so. |
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BP560 |
| There exists a closed trail that hits each edge exactly once vs. not so. |
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BP559 |
| Cross section of a cube vs. not cross section of a cube |
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BP558 |
| Point sequence that is increasing or decreasing in height vs. point sequence that alternates in height |
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BP557 |
| Equal horizontal length vs. not |
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BP555 |
| Black and white photograph versus drawing. |
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