Geometry has always fascinated mathematicians and philosophers alike. From the ancient Greeks to modern mathematicians, we’ve made incredible strides in understanding the world around us through geometry.
In this article, we explore a new kind of geometry, one that takes a step further from the Euclidean Geometry we all know and love.
Euclidean Geometry
Euclidean Geometry, named after the ancient Greek mathematician Euclid, is the basis for most of the geometry we learn in school. It is focused on flat spaces and deals with familiar shapes such as points, lines, and planes.
The key elements of Euclidean Geometry are:
- Points: A point is the most basic unit in geometry, representing a location in space.
- Lines: A line is an infinite collection of points, extending in both directions.
- Planes: A plane is a flat, two-dimensional surface that extends infinitely in all directions.
Line Segments
Line segments are the building blocks of many geometric shapes. They are finite sections of lines defined by two endpoints or an endpoint and some sense of magnitude. Understanding line segments is essential for grasping more complex geometrical concepts.
The Meta-Object Projection Hypothesis
In our newly proposed geometry, we take a mind-bending approach to understanding lines, planes, and other geometric objects.
We postulate that every line is actually a projection of a meta-object in another set of dimensions.
This projection occurs as the meta-object interacts with the two-dimensional space, casting a shadow that we perceive as a line. Similarly, other geometric objects are also projections of higher-dimensional meta-objects.
This idea opens up a world of possibilities, where the geometry we observe is merely a lower-dimensional representation of something much more profound.
The Mysterious Behavior of Regular Polygons in Higher Dimensions
In this new geometry, we explore a fascinating phenomenon: the behavior of regular polygons as the number of dimensions increases. We notice that the number of possible regular polygons increases until dimension four but decreases thereafter.
What could be the reason behind this enigmatic pattern?
T − E + V = 2. But more on this later.
… TO BE CONTINUED …
TS
06.06.23
Twishmay's Blog 
Leave a comment