Hi, one Professor gave me a very hard question, He has a little Disk (used in machines) that has a big hole in the middle, he measured the thickness every 90°, and he got the following measurements:
0.95 mm
1.02 mm
1.02 mm
0.96 mm
He tells me that with 3 of these measurements, I can know which is the maximum thickness and the minimum thickness even though he didn't measure the thickness everywhere, he wants to know the maximum and minimum thickness to know if the Disk has a big slope and may fail in the machine.
I would be really happy if you could help me with this one :)
I believe you have posted this question before. The reason you may not have got an answer, as far as I am concerned, is that the question is not complete. Perhaps your teacher did not provide the information because it was obvious for him.
For anyone to be able to calculate/predict the fourth thickness, or even the thickness at any point around the circumference, we need to know the "function" that governs the thickness. It could be a sine or cosine variation, or it could be anything else.
Given only 3 or four thicknesses on the circumference, we could fit an infinite number of functions and so calculate an an uncountable number of answers.
If I have misinterpreted your question, let me know.
I too have seen this post several times, and as PC stated above, was not able to follow the problem as stated.
Sure! I can help you solve this problem. To determine the maximum and minimum thickness of the disk using only three measurements, we can make use of a concept called the Extreme Value Theorem.
The Extreme Value Theorem states that a continuous function on a closed interval will have both a maximum and minimum value within that interval. In this case, we can consider the measurements as data points representing the thickness of the disk at specific angles.
Let's analyze the given measurements to find the maximum and minimum thickness:
1.95 mm
1.02 mm
1.02 mm
0.96 mm
To determine the maximum thickness, we need to find the highest measurement among the four given values. So, the first step is to compare each measurement with the others. Let's start by comparing the first measurement (0.95 mm) with the others:
- Is 0.95 mm greater than 1.02 mm? No.
- Is 0.95 mm greater than 1.02 mm? No.
- Is 0.95 mm greater than 0.96 mm? No.
Since 0.95 mm is not greater than any of the other measurements, we can conclude that it is not the maximum thickness.
Next, let's compare the second measurement (1.02 mm) with the others:
- Is 1.02 mm greater than 0.95 mm? Yes.
- Is 1.02 mm greater than 1.02 mm? No.
- Is 1.02 mm greater than 0.96 mm? Yes.
Based on this comparison, we see that the second measurement (1.02 mm) is greater than the first (0.95 mm) and the last (0.96 mm). However, it is equal to the third measurement (1.02 mm). As per the professor's statement, we only need three measurements to find the maximum and minimum thickness.
Therefore, we can conclude that the maximum thickness of the disk is 1.02 mm.
To find the minimum thickness, we can follow a similar process. We compare each measurement with the others:
- Is 0.95 mm less than 1.02 mm? Yes.
- Is 0.95 mm less than 1.02 mm? Yes.
- Is 0.95 mm less than 0.96 mm? Yes.
Based on these comparisons, we can determine that the minimum thickness of the disk is 0.95 mm.
Hence, the maximum thickness of the disk is 1.02 mm, and the minimum thickness is 0.95 mm.