The discussion revolves around the feasibility of measuring an irrational quantity, specifically ##\sqrt{2}## kg, using a scale. Participants explore the implications of irrational numbers in measurement and the accuracy limitations inherent in any measuring process.
The discussion is active, with various viewpoints being explored regarding the measurement of irrational numbers. Participants are questioning assumptions about the nature of measurement and the role of accuracy, with some providing counter-proposals and others emphasizing the limitations of standard scales.
Participants note that any measurement has a margin of error and discuss constraints related to the construction of objects representing irrational lengths. There is mention of imposed homework rules regarding the use of standard scales for such measurements.
It's impossible, but not because the number is irrational. To what accuracy do you propose that this measurement be made? Any measurement is impossible to make beyond a given accuracy.littlemathquark said:Because of ##\sqrt{2}## be a irational numbers I think it is impossible and there is no scales that can measure irational quantity. May be approximately. But 2 kg can be measurable. İt is my efforts and thougts.
I repeat, to what accuracy?pines-demon said:I will offer a counter proposal, make a square with side lengths equal to the unit of your choosing, make an object with the lenght of the diagonal of the square. Now your object has a length of ##\sqrt{2}## units.
As good as your square is. If you make it really straight, thermal fluctuations may average any irregularity out.kuruman said:I repeat, to what accuracy?
If it's impossible for ##\sqrt 2##, then it's impossible for any number. Every measurement has a margin of error.kuruman said:It's impossible, but not because the number is irrational. To what accuracy do you propose that this measurement be made? Any measurement is impossible to make beyond a given accuracy.
I don't see why not. You use your trick to get a length of ##\sqrt 2## and then use that on a scale.pines-demon said:Edit: What you are not allowed to do is take a regular scale and try to find ##\sqrt{2}## units in that scale.
No it doesn’t. You have an object that is ##\sqrt 2## units within the errors of your construction.pines-demon said:I will offer a counter proposal, make a square with side lengths equal to the unit of your choosing, make an object with the lenght of the diagonal of the square. Now your object has a length of ##\sqrt{2}## units.
On the contrary. Thermal fluctuations add to the construction error.pines-demon said:As good as your square is. If you make it really straight, thermal fluctuations may average any irregularity out.
obviously…PeroK said:If it's impossible for ##\sqrt 2##, then it's impossible for any number. Every measurement has a margin of error.
There is also thermal expansion.Orodruin said:On the contrary. Thermal fluctuations add to the construction error.