Will limit of discrete steps give Pythagoras theorem?

In summary, the conversation discusses the concept of moving along the sides of a right triangle, rather than the hypotenuse, and how it relates to the discreteness of space. The idea is that the distance moved is equal to the sum of the other two sides, even when taking infinitesimal steps. However, this argument is challenged by the fact that the limit of lengths of curves may not necessarily be equal to the length of the limit curve. A thread on this topic is also mentioned for further discussion.
  • #1
krishna mohan
117
0
Hi...

It is an easy to see fact that, instead of moving along the hypotenuse of a right triangle, one starts from the lower corner and reach the upper corner moving only along the directions of the other two sides, i.e only vertically and horizontally and not diagonally...the distance moved is just the sum of the other two sides...even if we take a limit of the steps being infinitesimal...
Somewhere I remember having read of this being an argument against discreteness of space...

Can someone throw some light on this topic??
 
Physics news on Phys.org
  • #2
I don't understand how that works. The problem is that the limit of lengths of curves isn't necessarily the length of the limit curve (I think you need smoothness for this). To illustrate, in your example, the limit of your "curves" is indeed the hypotenuse, but all of the intermediate curves will have length (base x height), so the limit of the lengths aren't equal to the length of the limit curve. Hope that makes sense!
 
  • #3

1. What is the limit of discrete steps in relation to Pythagoras theorem?

The limit of discrete steps refers to the smallest unit of measurement or distance that can be taken in a given system. In the context of Pythagoras theorem, it represents the smallest possible change in distance that can be measured between two points.

2. How does the limit of discrete steps affect Pythagoras theorem?

The limit of discrete steps plays a crucial role in Pythagoras theorem. It allows us to break down a continuous line or curve into smaller segments, making it possible to calculate the length of a diagonal line or the hypotenuse of a right triangle using only the lengths of its two sides.

3. Why is the limit of discrete steps important in geometry and trigonometry?

The limit of discrete steps is important in geometry and trigonometry because it allows us to accurately measure and calculate distances and angles in a given system. It is a fundamental concept in these fields, as it enables us to apply mathematical principles to real-world scenarios.

4. Can the limit of discrete steps be infinitely small?

Yes, the limit of discrete steps can be infinitely small. As our measuring tools and techniques continue to advance, we are able to break down distances into smaller and smaller increments, approaching an infinitely small limit of discrete steps.

5. How does the limit of discrete steps relate to the concept of a continuous function?

The limit of discrete steps is closely related to the concept of a continuous function. A continuous function is one that can be measured or traced without any abrupt changes or breaks. The limit of discrete steps allows us to approximate a continuous function by breaking it down into smaller and smaller segments.

Similar threads

I How fast does the particle go through spacetime?
    • Special and General Relativity
Replies
20
Views
2K
I Is the proof of the KRK endgame theorem rigorous and original?
    • General Math
Replies
13
Views
1K
Find Pythagoras Triples w/ Given Hypotenuse
    • General Math
Replies
3
Views
1K
'Average Distance' Between Many Points
    • Differential Geometry
Replies
9
Views
13K
I The far reaching ramifications of the work-energy theorem
    • Classical Physics
Replies
31
Views
2K
Roof truss -- distributed load
    • Engineering and Comp Sci Homework Help
Replies
3
Views
3K
I Elitzur–Vaidman bomb tester in multi-world interpretation
    • Quantum Interpretations and Foundations
Replies
21
Views
3K
I What is the limit of smallest size for a reliably working transistor in a computer chip?
    • Atomic and Condensed Matter
Replies
19
Views
2K
Egg tossing crime -- From what location was the egg thrown?
    • Introductory Physics Homework Help
Replies
14
Views
2K
I Explanation and clarifications in epsilon-delta limit proofs
    • Calculus
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top