Concerning a Difficulty in the Crescent
Problem… A square that has a side length of one unit is said to be inscribed with a circle. This length is equal to the radius of a quarter-circle. Determine the total land mass included inside as many of the various types of forms and areas as you can. (Which of these places or shapes do you find particularly challenging? What exactly is it that is preventing you from locating their locations?) Before Looking into the solution to this problem, you should answer, Is there a way to divide 5 into 3?
Students will generally specify the square, the inscribed circle, the quarter circle, and often a quarter of the circle as forms and regions to calculate the areas of, and they will then continue to do so without any problems. Students also take notice of the dark orange ‘crescent’ zone as an area to identify, as well as the lighter orange areas surrounding it. These regions outline the components of the issue that have the potential to evolve into the most formative conversations.
Students, of course with the assistance and support of the instructor, may sketch a plan of how to locate these more complicated places, oblivious to the fact that they may or may not yet have the information, abilities, or understanding to see such a strategy through to its completion. This may then lead into more direct instruction, or it can operate as a transition into a body of work that will offer students with the information and abilities they need in order to implement their technique. This will depend on where the students are in their mathematical careers.
Problem:
This issue was first presented as a “job interview question” in a discussion thread on Stack Overflow, where I discovered it. I am sorry to say that I cannot locate the query. But I was able to save the photo, and I have no idea how to use it.
The challenge here is to figure just how much space the crescent takes up.
1
Putting a dot and a label in the middle of an issue involving a circle is beneficial in virtually all of the cases when the problem involves a “diagram.” We have a name for the spot in the middle of the very large circle. Position at the exact middle of the more compact circle. — André Nicolas
Posted by user6312 on April 29, 2011, at 19:58 Because they imply that it was borrowed from another conversation, I don’t believe the OP came up with this number on their own. The name of Matthew Conroy
Apr 29, 2011 at 20:17
Someone who is applying for a job interview recently told me that they found the solution on this website, which I find to be rather humorous. Considering that I asked the query in the Programmers forum and didn’t realise there was already an answer provided online! Oh well, I guess I’ll just have to do some more studying for these examinations. – Orbling
Nov 6, 2013 at 15:33
I don’t get how CE may equal 4 plus x; can you explain where the 4 comes from? – shakram02
Sep 18, 2018 at 7:06 @shakram02: BC = CF. BC = 9 + x. CF = 5 + CE. So 5 + CE = 9 + x. So CE = 4 + x. – Aryabhata
Sep 19, 2018 at 1:22
@Aryabhata, it was a really nice and ingenious approach! My only criticism is that you omitted the step in which you arrived at the conclusion that CE = 4 + x. Perhaps you did this so that your answer would seem to be more succinct. However, this type of thing leads to confusion, and it is not at all acceptable while attempting to solve mathematical problems. – Apostolos
Sep 30, 2018 at 9:52
@Apostolos: Thanks! However, I am completely oblivious to the rationale for the skip. My response does change depending on the nature of the inquiry being asked. Seeing as how this was a question that was asked during an interview, I suppose it was OK for me to leave out certain stages. – Aryabhata Oct 5, 2018 at 23:46
If you were to write this answer on a high school exam, you would receive a grade of C or D only for that, because you would not have supported your statement with proof!:) I’ve never had a math interview, so I don’t know how they go. However, I do know that if you were to write this answer, you would receive a grade of C or D only for that. — Apostolos Leibovici on October 7, 2018, at 15:50
