I am a field service engineer and the most math I need to know is to make sure there are not too many nodes connected to an access point. My girlfriend is working on her masters in physics. She thinks we need to take an interest in each others hobbies Ok mine is saltwater reef aquariums, hers is mathematics. She enjoys it so much she even volunteers her time to teach at an adult education center. Now onto my problem; She came up with a math problem and asked me how I would solve it. You bought a old circular table and the top there was only less than half left. How do you figure out the exact diameter of what the table was. Ok what little I do remember from high school I know that a perpendicular bisector will pass thru the radius of a circle. Thinking I am smart for once I said I would draw two bisectors and at the point of intersection I could measure that and multiply by 2 this would give me the diameter. That was not the answer she wanted she wants to know how this could be solved using only a tape measure and math. After some time I gave up and she told me that I could use A squared + B squared = C squared Pathagareum (SPL) theory. I have looked this over several times and I see no right angles. Is she correct or did she for once make a mistake and there is another way? Probably not but If she is correct perhaps someone can explain it..
Thanks in advance
Sorry, you'll have to do your part of work. I am not relying on you knowing all these shapes by name. I myself always confuse sector and segment. But did you follow the links in post #2? Which picture given there is most similar to your shape?
If you are allowed to measure the height h of the circular segment as well its chord (base) length c, then the diameter is
This page has this formula along with its derivation. The height h can be found by finding the middle of the chord and setting up a perpendicular to the chord at that point. If you can't measure the height since you don't have a carpenter's square or a protractor and if you can only use the tape measure to measure s and c, then apparently you can't write a simple formula for the diameter. Instead, you'll have to solve one equation numerically and then express the diameter through the result. This is described in Dr. Math forum.
The derivation of the formula for the diameter above uses a theorem about chords. I don't have time right now to find out if it can be derived using the Pythagorean theorem, but I may come back to this later.