Flatland Analysis

In the story Flatland: A Romance of Many Dimensions, written by Edwin A. Abbott, there are many dimensions in which the main character, A. Square travels. Throughout the traveling of this square, we learn about how many of the different societies function and how they respond. Many of these events as mentioned in Flatland, still occur today or have occurred in the past. Some of these parallel events between our society and the ones mentioned in Flatland often revolve around religion or beliefs. This is exposed in the novel through the meeting of A. Square and Lord Sphere, the Colour Bill, and A. Square’s return to Flatland.

The meeting of A. Square and Lord Sphere was similar to events in today’s society. When the shapes tried to explain to

The colour bill was a way for shapes to color their sides so that it was easier to distinguish between the different shapes. However many people supported the idea, many did not as well. This Bill would allow women to be colored the same way as priests. When the women learned of this, they were happy as they may be perceived as males and treated more fairly. The priests were not in support of this idea. They did not want to be perceived as or confused with females. They believed they were of higher social order and they did not want to be looked upon as a lesser being than they were. This parallels events taking place in our society as often times, there are groups who do not agree on a subject. For example, many people believe that no matter the color of one’s skin, everyone should be treated equally. There are also groups of people that are advocating for a specific color to matter more than others as in the Black Lives Matter campaign. Although many people support this, many still do not. They want to believe that they are of higher standard and should be treated as such. The colour bill is a current example of a disagreement within the human

In Euclidean triangles, all of the interior angles add up to equal 180° however in Hyperbolic triangles, the interior angles add up to equal less than 180° (Cornell). This is due to the fact that all of the lines are curved (Quora). Continuing, in Euclidean triangles, if two triangles are similar, then they only have to have equivalent angles and not necessarily congruent sides. In Hyperbolic geometry, if two or more triangles are considered similar, they will be congruent (Cornell). Finally, in Hyperbolic geometry, two triangles will have the same area if and only if their angle sums are the same (Cornell). We know this is not true in Euclidean geometry since all triangles have the same angle sum of 180°. Finally, Hyperbolic has some practical applications in our 3-dimensional world. Examples of these applications include art and the design of many practical things. Many artists have used Hyperbolic geometry to make art on the circular plane as mentioned before. An example of one of these paintings includes work belonging to M.C. Escher.

(Cornell)

Secondly, Hyperbolic geometry has the use of something called a Hyperbolic paraboloid (Postulate-Posse). This is a curved design that has been used to make the shape for a horse's saddle or even a Pringles® chip. The shape of the paraboloid is as follows:

In conclusion, Hyperbolic geometry is present in many day to day things around