The Art of Frost: Reflecting on Shadows in Ice Sculptures

A curve of shadows and ice The phrase "a curve of shadows and ice" evokes a vivid image of a landscape formed by contrasting elements of light and dark, warmth and coldness. This description brings to mind a scene where shadows cast by various objects create a curved shape, while ice glistens in the background. Such a landscape could be found in wintry regions where the ground is covered in a blanket of snow and ice. The curves formed by the shadows suggest a sense of movement and dynamism within this frozen setting. It is as if the shadows themselves are flowingly meandering across the frozen surface. The play of light and dark adds an element of mystery and intrigue to this scene.

The play of light and dark adds an element of mystery and intrigue to this scene. Shadows have long been associated with the unknown, the hidden, and the subconscious. They create an atmosphere of suspense and invite the imagination to fill in the gaps between what is seen and what is hidden, resulting in a sense of curiosity and wonder.

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? $\endgroup$

The presence of ice in the background adds another layer of complexity to this imagery. Ice is often associated with clarity, resilience, and transformation. It reflects light in a beautiful and captivating way, adding a glimmering quality to the overall scene. The juxtaposition of shadows and ice creates an interesting interplay between light and dark, warmth and cold, movement and stillness. Overall, the phrase "a curve of shadows and ice" paints a captivating picture of a wintry landscape filled with contrasts and hidden depths. It implies a scene that is both visually stunning and emotionally engaging, inviting viewers to explore and contemplate the interplay of light and shadow, warmth and coldness, within a frozen setting..

Reviews for "Life in the Shadows: Surviving and Thriving in Ice-covered Environments"

1. Karen - 2 stars:

I had high hopes for "A Curve of Shadows and Ice" as I'm a fan of the fantasy genre, but unfortunately, this book fell short of my expectations. The plot was confusing and hard to follow, with multiple storylines that never seemed to come together in a satisfying way. The characters were also very one-dimensional and lacked depth, making it difficult to connect with any of them. Overall, I found the book to be unengaging and lacking originality.

2. John - 1 star:

I found "A Curve of Shadows and Ice" to be a tedious read. The pacing was incredibly slow and the descriptions were overly detailed, leaving little room for imagination. The world-building was also lackluster, with minimal information provided to understand the setting and its rules. The dialogue felt forced and unnatural, making it hard to believe in the interactions between characters. I struggled to find any enjoyment in this book and wouldn't recommend it to others.

3. Sarah - 2 stars:

I was really looking forward to reading "A Curve of Shadows and Ice" but was ultimately disappointed. The writing style was dry and lacked the necessary flair to bring the story to life. The characters were forgettable, and their actions often felt forced and unrealistic. The magic system introduced in the book was convoluted and poorly explained, leaving me confused and disinterested. Overall, the book failed to capture my attention and failed to deliver an engaging fantasy experience.

4. Mark - 1 star:

"A Curve of Shadows and Ice" was a complete letdown. The plot was predictable and lacked any surprises or twists. The characters were bland and lacked any interesting personalities. The dialogue was wooden and unnatural, making it difficult to feel any emotional connection to the story. The author failed to create a captivating world, leaving the setting feeling mediocre and unremarkable. I regret spending my time on this book and would advise others to skip it.

The Hidden Symphonies: Exploring the Sound of Shadows on Ice