Crystal frames problem, what actually asking?

In summary, the conversation is about a problem from the Sterway, Jewett book that the person is having trouble understanding. They mention that the answer in the book is 0.141 nm, but they cannot achieve it. They also mention that there are too many unnecessary problems in the book. Another person then provides a solution involving the distance between vertical or horizontal planes and 45 degree planes. The person who was stuck then solves the problem on their own and expresses their happiness.
  • #1
frostysh
63
3

Homework Statement



The problem from Sterway, Jewett book.

Serway_Jewett_problem_Mech_Crystal1.jpg


Serway_Jewett_problem_Mech_Crystal2.jpg


The Attempt at a Solution



The answer in the book is something like 0,141 nm, as I remembered but I cannot achieve such answer coz' I cannot understand what actually asking, d is looks like a distance between two centers of the atomic spheres, but I don't think that it can be 0,141 nm, probably due to my English language, so can somebody clarify for little bit, what the hell I need to find in this problem. I am stucked for now, and my brain will start to melt soon. And imho - this book have too much of unnecessary problem, 70 problem for the first chapter is too much... Thanx.
 
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  • #2
In the same way as the distance between vertical or horizontal planes is L, the distance between the 45 degree planes is ##{1\over 2}\sqrt 2 ## L. Easiest seen in a side view:
upload_2017-5-5_16-15-39.png
 
  • #3
BvU said:
In the same way as the distance between vertical or horizontal planes is L, the distance between the 45 degree planes is ##{1\over 2}\sqrt 2 ## L. Easiest seen in a side view:
View attachment 198771
Or this picture in the book is distracting, or frostysh is just too dull :), anyway I have solved the problem on my new cool self-made school-board, and now I am very happy ^^. Thanx again, Solved.
 

1. What is the "Crystal frames problem"?

The Crystal frames problem is a mathematical problem that involves finding the optimal arrangement of identical rods or frames in a given space. It is often used as a teaching tool for discussing mathematical concepts such as symmetry and optimization.

2. Why is it called the "Crystal frames problem"?

The problem is named after the way crystals form, with repeating patterns and symmetries. The rods or frames in the problem are arranged in a similar way, creating a crystal-like structure.

3. What is the purpose of solving the "Crystal frames problem"?

The Crystal frames problem is often used as a way to introduce students to mathematical concepts and problem-solving techniques. It also has real-world applications in fields such as architecture and materials science, where finding the most efficient arrangement of objects is important.

4. Can the "Crystal frames problem" be solved for any number of rods or frames?

Yes, the problem can be solved for any number of rods or frames. However, as the number of rods increases, the problem becomes more complex and may require advanced mathematical techniques to find the optimal solution.

5. Are there any practical applications for solving the "Crystal frames problem"?

Yes, there are several practical applications for solving the Crystal frames problem. For example, it can be used to determine the most efficient way to stack boxes in a warehouse or to design the layout of molecules in a crystal structure. It can also be applied to optimize the placement of solar panels or antennas on a satellite.

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