In Edwin E. Slosson's "Easy Lessons in Einstein," Section 7 titled "Non-Euclidean Geometry, Some Simple Examples" would likely delve into the complex realm of geometry that steps outside the traditional Euclidean framework. Given the book's focus on making Einstein's theories accessible, this section would be crucial for explaining how Einstein's General Theory of Relativity incorporates the principles of non-Euclidean geometry to describe the structure of space and time.

Potential Content of "Non-Euclidean Geometry, Some Simple Examples"

Here's a generalized outline of what Section 7 might cover:

1. Introduction to Non-Euclidean Geometry: Slosson would likely start with a brief history and explanation of what constitutes Non-Euclidean geometry. This includes defining the differences between Euclidean geometry, which deals with flat surfaces, and Non-Euclidean geometries, which concern themselves with curved surfaces. This discussion would provide a fundamental understanding of how traditional geometric rules (like the parallel postulate) are altered in Non-Euclidean contexts.

2. Relativity and Geometry: This section would explain how Non-Euclidean geometry is relevant to Einstein’s theory. It could illustrate how the curvature of space-time, a central tenet of General Relativity, is described using the mathematical language of Non-Euclidean geometry. Slosson might include simple analogies, such as the bending of light around a massive object, to show how space itself can be curved.

3. Simple Examples: To make these concepts tangible, Slosson could offer simple, everyday examples of Non-Euclidean geometry at work. For instance, he might describe the surface of a sphere (like Earth) to explain how traditional "straight lines" (geodesics in geometry) such as the equator or the lines of longitude, do not behave as they do in flat, Euclidean space. These examples would help illustrate how straight paths on a curved surface can converge or diverge, unlike parallel lines in Euclidean geometry.

4. Implications for Physics: Further, the section would discuss how these geometric concepts underpin more complex ideas in physics, such as gravitational fields and the orbit of planets and light around stars. Slosson could discuss how Einstein used Non-Euclidean geometry to predict phenomena that were later confirmed, like the bending of starlight by the sun observed during a solar eclipse.

5. Conceptual Challenges: Lastly, Slosson might address the intellectual shift required to accept and understand Non-Euclidean geometry. This would involve a discussion on the challenges and resistances faced by mathematicians and physicists in adopting these models, emphasizing the progression from theoretical mathematics to practical, observable physics.

By the end of this section, readers of "Easy Lessons in Einstein" would have a foundational understanding of Non-Euclidean geometry and its critical role in modern physics, particularly in the theory of relativity. Slosson’s approach would likely be to demystify these ideas, making them accessible and engaging to readers without a background in advanced mathematics.