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Sphereland: A Fantasy about Curved Spaces and an Expanding Universe
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Sphereland: A Fantasy about Curved Spaces and an Expanding Universe

3.61 of 5 stars 3.61  ·  rating details  ·  270 ratings  ·  23 reviews
A short Science Fiction novel by a distinguished Dutch mathematician which entertains and instructs in the multi-dimensional geometries of curved space and the expanding universe.
Paperback, 222 pages
Published June 1st 1983 by HarperCollins Publishers (first published 1965)
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The sequel to Flatland. This one was written by a Dutch mathematician in 1960. Flatland was written in 1881, before relativity and quantum, and while ingenious in concept, its physics and geometry had obvious flaws. However, the first thing that Burger feels compelled to correct in this book is the status of women. This story is told by the grandson (a Hexagon) of the Square who narrated Flatland. He goes to great length ensuring us that things have changed in Flatland, and women, even though st ...more
Using our view of a two-dimensional world as a model, Burger attempts to show us what we cannot see about the limitations of our own 3-D world from the perspective of a 4-D one. Moving constantly between the 1-D world (Lineland) to the 2-D world (Flatland), our current experience in the 3-D world (Sphereland) is the jumping-off point to begin comprehension of the 4-D world. Unfortunately, like the characters in the novel, we too are limited in our ability to visualize the dimension above us, but ...more
Joe Labriola
Further building upon the canon of modern geometrical fantasy as established by the brilliantly insightful Edwin A. Abbott in his classic, "Flatland", "Sphereland" is a daring sequel by Dionijs Burger Jr. - a story that creatively if sometimes confusingly challenges what we think we know about the physical reality of the world around us, including our own dimension as well as those far beyond our limited perceptions as "3D" beings.
Ton van Gessel
Een vervolg op flatland de flatlanders realiseren zich dat ze op het oppervlak van een 3 dimensionaal oppervlak leven ..... je ziet de analogieën al denk ik.
As a sequel, and expansion (no pun intended) on the ideas presented in Flatland I thought, eventually, this book had something to offer. It did provide me some insight into the ideas of curved space and an expanding universe. My critique is that it took too long to get there and there was a lot of superfluous elements like the reselling of fairy tales. I didn't think it used the Flatland setup in an inventive way. It essentially copied what happened in that book, multiple times over, changing th ...more
In the 1960s a Dutch mathematician, Dionys Burger, decided to attempt updating E.A.Abbott's 1890s classic fantasy on dimensional mathematics. Not quite as surprising and fun as the original Flatland, Sphereland nonetheless works well as a sequel. Burger attempts to include some of the changes in our view of spatial geometry since Einstein, while keeping to the simple dialogue approach of Abbott. If Flatland hadn't already seen the light of day nearly a century earlier, Sphereland would still sta ...more
This is about the only GOOD sequel to "Flatland". It takes the next logical step, which was to take the flat 2-D world of "Flatland" and have the denizens begin to infer, from large surveys, that their world is "curved" (on a sphere). They can't SEE the curvature, but can see that their largest triangles don't add up to 180 degrees. Brilliant! It helps understand how we 3-D creatures could "infer" that our world is curved in 4-D but not be able to SEE that curvature.

The main character here is descended from the main character in "Flatland" by Edwin A. Abbott and the story picks up soon after the end of the first book. This time the inhabitants, with the help of the Sphere from before, learn their world isn't flat at all, it's curved. o_O

More educational and much more entertaining than the excreble "An Episode of Flatland" by Charles Howard Hinton. If you enjoyed Flatland, you will love this one.
At the time of me writing this review, I have not yet read "Flatland" except for a few parts.

This sequel to "Flatland," written in 1960, is quite a worthy one. It expands on the Flatland universe, giving much better thought to gender roles, societal roles, and the notion of the real-world Big Bang Theory and the expanding universe, showing that our worlds, whether Flatland or the real universe, are more than what we see.
This was a bit slower and not as entertaining as "Flatland" especially with the last 30 pages or so.
The square's grandson is the writer now, explaining that his grandfather's views of a 3rd dimension are now allowed, but his views of an expanding world on a curved plane are not. This delves into non-Euclidean geometry, so that was fun.
Nick Black
Edwin Abbott ought step up from his musty grave and administer a crushing curby on Dionys Burger for raping his quaint Flatland: A Parable of Many Dimensions. Let this be a lesson to all of us about trusting people with such ridiculous first names. Dionys? GOMBIZ.
Amusing and readable. The social commentary parts were somewhat heavy-handed; the math parts were most excellent. Non-Euclidean space is interesting; when I set out to learn more about it I'll be glad to have this accessible tome to refer to.
slow going, because seemed to repeat the premise and beginning plot of Flatland, but it finally got going around 3/4 through! Fun analogies to our 3-dimensional space, and a fun not-so-metaphorical look at our own grapple with space-time.
Oct 19, 2007 Liz rated it 5 of 5 stars
Recommends it for: EVERYONE!
flatland started it... sphereland really stretches your imagination's flexibility and the language it is written in is much more accessible. for dreamers, artists, mathematicians and anyone interested in being alive and musing about it!!!!!
Another cute spin off from Flatland. It really should be read before "Flatterland". I liked his descriptions of life in Flatland and his histories and fairy tales. The math and science themselves, not so much.
Dec 26, 2013 Eric rated it 4 of 5 stars
Shelves: math
I enjoyed the novel. I liked the expansion on non-Euclidean geometry and the thought of an expanding sphere at the end. The way the book intertwines various well known stories was a nice touch.
Tedious, teaching the wrong idea about how scientific discovery works, and entirely missed the point of the social commentary of the original. Asimov's intro to both was way off the mark.
Lea Patrick
If you liked Flatland, you will LOVE Sphereland!!! Open your mind when you open this book and your perception will open with it! Truly an awe inspiring read!
So far, I've learned that they feel badly about the negative portrayal of women and Flatland....and space is curved...
Still more interesting stuffs.
Oct 26, 2011 Steven marked it as to-read
Follow up to Flatland.
Building on Abbott's Flatland, this one expanded my horizons regarding the third dimension, the fourth, and beyond.
May 23, 2010 Hamed added it
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Silvestergespräche eines Sechsecks. Ein phantastischer Roman von gekrümmten Räumen und dem sich ausdehnenden Weltall Locke's Bewijs Voor Het Bestaan Van God (1872) Commentarius in Ecclesiasten: In Usum Juventutis Academicae Prolegomena Et Annotationem in Theaetetum Platonis Dialogum, Scripsit D. Burger Flatland & Sphereland

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