gems of war delve guide

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In folklore and literature, the Fairy King is often depicted as a powerful and enigmatic ruler of the fairy realm. He is known for his strange and mysterious abilities, which are often referred to as "strange magix." This term emphasizes the otherworldly nature of the Fairy King's powers and the limits of human comprehension when it comes to understanding them. The Fairy King's magic is often described as unconventional and unpredictable. It is said to be deeply rooted in nature, allowing him to manipulate the elements, control the weather, and influence the growth of plants and animals. However, his magic is not limited to the natural world; he is also believed to have powers over illusion and transformation.

A curve of shadows and ice

However, his magic is not limited to the natural world; he is also believed to have powers over illusion and transformation. This enables him to change his own appearance or create illusions to deceive and bewilder humans. One of the most fascinating aspects of the Fairy King's magic is its connection to time and space.

Is the sphere the only surface with circular projections? Or: Can we deduce a spherical Earth by observing that its shadows on the Moon are circular?

We had a great time discussing the question after our logic seminar here in New York this week, when our speaker Maryanthe Malliaris asked the spherical Earth question.

December 20, 2010: In light (or dark, as it were) of the lunar eclipse tonight, I am bumping this question, with the remark also that despite the truly outstanding answers we have received, several of the further questions stated above are not fully answered.

  • mg.metric-geometry
Cite Follow 169k 16 16 gold badges 409 409 silver badges 588 588 bronze badges asked Sep 17, 2010 at 18:02 Joel David Hamkins Joel David Hamkins 216k 40 40 gold badges 701 701 silver badges 1238 1238 bronze badges $\endgroup$

$\begingroup$ I've often heard that we can deduce a spherical Earth by observing that its shadows on the Moon are always circular - but always without proof, and in non-mathematical sources where it wouldn't be obvious that proof is necessary. $\endgroup$

Sep 17, 2010 at 18:42

$\begingroup$ What is the "set of shadows"? Do you know which projection gives which shadow, or just an unstructured set of planar shapes? $\endgroup$

Sep 17, 2010 at 18:45

$\begingroup$ I had meant the set of planar shapes, without knowing in which direction the projection is taken. $\endgroup$

Sep 17, 2010 at 18:47

$\begingroup$ Perhaps Joel can add this to his generalizations. Suppose we have a catalogue of information which may be a proper subset of the following: for each 2-D projection of a 3-D object, we have the list of widths ( and perhaps directions ) for that projection. How much of the catalogue do we need to reconstruct the original (let's assume convex) object? Note this may be different from knowing bounding hyperplane distance in a given direction for all directions, as the catalogue might be indexed by projection. Or is it the same? Gerhard "Ask Me About System Design" Paseman, 2010.09.17 $\endgroup$

Sep 17, 2010 at 20:33

$\begingroup$ Gerhard, your suggestion is indeed in the spirit of my further questions. For the catalogue, I suppose we could imagine living on the object, and occasionally being able to observe part of a projection, from an essentially random direction, thereby simulating in part the shadow-of-the-Earth-on-the-moon situation. To what extent can we deduce the shape of the object from this information? $\endgroup$

Sep 17, 2010 at 22:31
Gems of war delve guide

He is often associated with the ability to bend or manipulate reality, causing time to move differently within his realm. This can result in humans entering the fairy world for what feels like a few hours, only to return to their own world and discover that several years have passed. Similarly, the Fairy King is said to have the power to create portals or gateways between different dimensions, allowing him to travel between worlds at will. However, there is a sense of caution surrounding the Fairy King and his magic. While he may initially appear benevolent and generous, he is also known for his capricious nature. Like the fairies themselves, the Fairy King can be mischievous and unpredictable, often subjecting humans to trickery or placing them under mysterious spells. It is believed that he takes pleasure in testing the limits of mortal resilience and the human capacity for wonder. Overall, the Fairy King's strange magic is a captivating and intriguing aspect of fairy folklore. It highlights the boundary between the human and fairy worlds, reminding us of the mystery and enchantment that exists just beyond our everyday perception. Whether portrayed as a noble and wise ruler or a mischievous and unpredictable trickster, the Fairy King and his peculiar magic continue to captivate our imagination and fuel our fascination with the supernatural..

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gems of war delve guide

gems of war delve guide

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