Higher Dimensions and the Roles of Length, Area, and Volume - Rational Geometry Math Foundations

Explore the fundamental concepts of higher-dimensional geometry in this 29-minute video lecture. Delve into the roles of length, area, and volume, challenging the conventional understanding of these measurements. Discover how quadrance, quadrea, and quadrume serve as more general and fundamental replacements for traditional measurements. Examine the geometric nature of linear structures in different dimensions, including the intriguing possibility of exact equilateral triangles in three-dimensional space. Learn about the importance of rational numbers in geometry, signed versions of measurements, and the concept of quadrance. Investigate the limitations of physical intuition and the significance of number theory in geometric understanding. Gain insights into topics such as tetrahedra, coordinate systems, and the isotropy conundrum, concluding with an exploration of the two-dimensional Cartesian plane.

Intro to measurements in geometry
Restriction to rational numbers in geometry
Signed versions of length, area and volume
Tetrahedron
Exercise
Quadrance exists when lengths do not
The price we pay for co-ordinates
The isotropy conundrum
Two dimensional Cartesian plane