nhl octopus

The magic tikt PWC trailer is a versatile and innovative product designed to make transporting personal watercrafts (PWCs) easier and more convenient. It is specifically designed to fit various models and sizes of PWCs, ensuring a secure and safe towing experience. One of the key features of the magic tikt PWC trailer is its lightweight and durable construction. The trailer is made from high-quality materials that can withstand the rigors of road travel while keeping the weight as low as possible. This makes it easier to tow the trailer with a vehicle and reduces fuel consumption. The magic tikt PWC trailer also comes with a multi-angle loading design that allows for easy on and offloading of the watercraft.

The magic tikt PWC trailer also comes with a multi-angle loading design that allows for easy on and offloading of the watercraft. This is especially useful when dealing with different types of PWCs and varying water conditions. The trailer can accommodate various sizes and shapes of PWCs, ensuring a secure fit and a smooth towing experience.

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

$\begingroup$ 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. $\endgroup$

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

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

$\begingroup$ 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 $\endgroup$

$\begingroup$ 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? $\endgroup$

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nhl octopus