Help: Reframing Buffon's Needle Problem

Hello, It was on 14th March on Pi day that I got to know about Buffon's needle problem:

Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?

It was worth noticing that how π can come up in unexpected situations. I saw the solution and it was quite easy and straightforward to understand.

By taking d1d_1 as the distance from the nearest line and θθ as the acute angle between the needle and the projected line with length d2d_2. We integrated the 2 variable and the probability was 2LπT\boxed{\frac{2L}{πT}} where LL is needle length and TT is the equal distance between the strips and L<TL < T.

Now, I reframed the question as :

Suppose we have a floor made of parallel as well as perpendicular strips of wood , each the same width, forming squares and we drop a needle onto the floor (needle is shorter than the width). What is the probability that the needle will lie across a line between two strips?

I tried by taking d2d_{2} as the horizontal distance and tried to calculate it by taking triple integration of those 3 variables but I am unable to approach it.

Please help me to approach this problem.

#Calculus

Note by Mohd. Hamza
2 years, 3 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list
  • bulleted
  • list

1. numbered
2. list
  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai−1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 ∑i=13 \sum_{i=1}^3
\sin \theta sin⁡θ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

You may want to refer to Buffon's needle problem and this.

Chew-Seong Cheong - 2 years, 3 months ago

Log in to reply

Thanks, so the reframed problem is actually Laplace-Buffon Needle Problem.

Mohd. Hamza - 2 years, 3 months ago
×

Problem Loading...

Note Loading...

Set Loading...