We know that earth is almost spherical in shape but when we move on earth it appears as flat. The reason behind this fact is “the larger the circle the smaller would be the curvature”. Prove this fact.
The correct answer and explanation is :
To prove that “the larger the circle, the smaller the curvature,” we use the mathematical concept of curvature for a circle.
Mathematical Proof:
The curvature ( K ) of a circle is given by the formula:
[
K = \frac{1}{R}
]
where:
- ( R ) is the radius of the circle.
- ( K ) represents how much the curve deviates from being straight.
From this equation, we see that curvature is inversely proportional to the radius. That means:
- If the radius ( R ) increases, the curvature ( K ) decreases.
- If the radius ( R ) decreases, the curvature ( K ) increases.
Explanation (300 Words):
The Earth is nearly spherical in shape, meaning it has a very large radius (about 6371 km). Since the curvature of a circle (or sphere, in this case) is given by ( K = 1/R ), Earth’s curvature is extremely small compared to our daily experience.
When we move on Earth’s surface, our field of view is very small relative to Earth’s size. If we take a small portion of a huge sphere, it appears almost flat. This is because the local curvature is so small that it is almost imperceptible to the human eye.
To understand this, consider a simple analogy:
- A small ball (like a marble) has a high curvature, meaning its surface noticeably bends.
- A large ball (like a giant exercise ball) has a lower curvature, so its surface appears less curved.
- If the ball were as large as the Earth, the curvature would be so small that standing on it would feel just like standing on a flat surface.
This principle is why Earth appears flat in our daily experience. However, when observed from space, the entire Earth appears clearly round. This difference is a direct consequence of the mathematical relationship between curvature and radius.