In geometry, the Egan conjecture gives a sufficient and necessary condition for the radii of two spheres and the distance of their centers, so that a simplex exists, which is completely contained inside the larger sphere and completely encloses the smaller sphere. The conjecture generalizes an equality discovered by William Chapple (and later independently by Leonard Euler), which is a special case of Poncelet's closure theorem, as well as the Grace–Danielsson inequality in one dimension higher.
The conjecture was proposed in 2014 by the Australian mathematician and science-fiction author Greg Egan. The "sufficient" part was proved in 2018, and the "necessary" part was proved in 2023.
In geometry, the Eganconjecture gives a sufficient and necessary condition for the radii of two spheres and the distance of their centers, so that a...
to also hold in higher dimensions, which later became known as the Eganconjecture. A proof of the inequality being sufficient was published by him in...
(hold-in, pull-in, lock-in ranges) coincide.: 4–5 Various conjectures (e.g., Egan'sconjecture on the pull-in range of type II APLL) and estimates of the...
pattern is a repetition of some smaller pattern. He also observed that this conjecture would imply the existence of an algorithm to decide whether a given finite...
extensive study. Arguably, the largest unproven conjecture in graph labeling is the Ringel–Kotzig conjecture, which hypothesizes that all trees are graceful...
September 2003, accessed 19 December 2012 Egan 1999, pp. 1–16. Orrell 1989. Mulryne; Shewring (1997: 37; 44) Egan 2004, pp. 5.1–22. Astington, John (2014)...
from the original on October 21, 2023. Retrieved October 21, 2023. Loo, Egan (November 27, 2019). "Top-Selling Light Novels in Japan by Series: 2019"...
it is not a coinage by the editor, H. P. Trefethen) is unclear.” The conjecture of editorial invention is further supported by the spurious explanation...
the TVA, refuse to interfere in events in time. Chronology protection conjecture, an hypothesis in physics Thor vol. 1 #372 (October 1986). Marvel Comics...
have occurred but are resolved differently than in actual history. As conjecture based upon historical fact, alternate history stories propose What if...
As used in this article, "posthuman" does not necessarily refer to a conjectured future where humans are extinct or otherwise absent from the Earth. Kevin...
subjective experience of surviving quantum suicide. This concept is sometimes conjectured to be applicable to real-world causes of death as well. As a thought...
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Great Plains. However, when at last he reached this place (variously conjectured to be in modern Kansas, Nebraska, or Missouri), he found little more...
Lawrence S. Cunningham, Keith J. Egan 1996 ISBN 978-0-8091-3660-5 pages 38–39 An Anthology of Christian mysticism by Harvey D. Egan 1991 ISBN 0-8146-6012-6 pages...
presented in the play as acting the part of Friar Tuck. Some scholars have conjectured that Skelton may have indeed written a lost Robin Hood play for Henry...
proclivities. Just what these traits are exactly is a matter of great debate and conjecture. Postgenderism is not concerned solely with the physical sex or its assumed...
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