My name is Caleb, I am 12 years old and going into 8th Grade. I will be taking a geometry course next year and my dad suggested coming here for a Summer assignment. What would be some good assignments (links, advice, observable experiments, etc.) that would prepare me for my geometry course?
Reading through a geometry book will be useful. For example, Euclid's elements is a classic book which defined mathematics for centuries to come (and it still continues to be relevant). You might try reading it. There are other (more modern) books on geometry too.
Thank you for answering my question. I will purchase Euclid's Elements. http://www.amazon.com/Euclids-Eleme...=1402263231&sr=1-1&keywords=euclid's+elements This is the link to the Euclid's Elements book and I wanted to make sure with you that this is the right one. After reading this book are there any practical assignments I can get from this book to present to my father? My father also says that observable experiments are extra-credit.
You can play around with these puzzles if you like. As for an observable experiment, an idea I have is to build a sundial (cardboard, pencil, putty), then place a mark at the end of the shadow at 30 minute intervals (hourly is probably better), finally trace out the path of the sun. Just an idea. Your dad sounds really strict...
Thank you for your help! My dad is not very strict. What happened was I made a deal with my parents that if I wanted privileges to hang out with my friends I had to get a 3.8 GPA at the end of my semester but ended with a 3.5 GPA. Since I did not meet the requirements my parents are giving me extra projects to gain these privileges. After reading Euclid's Elements I will reply to you on how the book was. Thank You, Caleb
About experiments you can do. A lot of proofs in the Elements offer specific constructions of things. For example, it shows you how to construct a triangle with all sides equal. It might be nice to do these constructions in geogebra. Geogebra is a very awesome computer program that will allow you to experiment with geometry and other math. It's completely free too: http://www.geogebra.org/cms/nl/ See if you can learn how to work with geogebra and see if you can reconstruct the proofs in Euclid using the tools of geogebra. Also, about the Elements. Don't go too far with it. There are about 13 books, but most of the later books are severely outdated. This is because geometry was the supreme science in Euclid's time and they didn't really trust algebra. Things like ##\sqrt{2}## were not accepted at the time. Euclid has then proceeded to construct a very tedious and inelegant theory that deals with ##\sqrt{2}## in a geometric way. This is only interesting from a historical perspective. Also, read with a critical mind. Many things in Euclid can be criticized by the modern reader for being flawed. This is why you also want some commentary on the book. The amazon link you provided is fine, but doesn't contain such commentary. The following book gives some commentary on Euclid and you can perhaps try to read it concurrently with Euclid: http://www.amazon.com/Geometry-Euclid-Beyond-Undergraduate-Mathematics/dp/0387986502
This is a very different situation. The recommendations I gave were for a student (your age perhaps) very interested in mathematics. We get such people regularly and they ask for books to self-study the material. Reading something like Euclid is very difficult but they can handle it because they're interested. However, you seem to want to do geometry because you're essentially forced by your father. Not that that's a bad thing. But do you like mathematics at all? Are you interested in geometry? How capable are you in mathematics? If you're just interested in getting your priveleges back and not really in geometry (which is perfectly acceptable, I'm not judging you), then you shouldn't read Euclid. There are easier books for you to do which you might find more interesting. If you're not interested in mathematics or are not very good in mathematics, then please do not do Euclid.
I find math very fun to do. I really like studying math and it is my favorite subject in school. In fact, if I don't make my first job all my backup jobs involve math, so I can have fun while doing my job. Also ever since I started middle school I have been working on Math parts which were 2 years above my level. Such as my 7th Grade year I was in Algebra 1 and in 6th Grade I was in Pre-Algebra. Also I am going into 8th Grade taking a Geometry class, which is a 10th Grade subject.