art of problem solving geometry class

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Art of Problem Solving Introduction to Geometry

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Learn the fundamentals of geometry from former USA Mathematical Olympiad winner Richard Rusczyk. Topics covered in the book include similar triangles, congruent triangles, quadrilaterals, polygons, circles, funky areas, power of a point, three-dimensional geometry, transformations, and much more.  

The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which geometric techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains over 900 problems. The solutions manual contains full solutions to all of the problems, not just answers.  

This book can serve as a complete geometry course, and is ideal for students who have mastered basic algebra, such as solving linear equations. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of geometry will find this book an instrumental part of their mathematics libraries.

This set includes both the lessons and solutions manuals.

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Art of Problem Solving Introduction to Geometry Textbook and Solutions Manual 2-Book Set Paperback – January 1, 1965

• Language English
• Publisher Art of Problem Solving
• Publication date January 1, 1965
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• ASIN ‏ : ‎ B0083C89NW
• Publisher ‏ : ‎ Art of Problem Solving (January 1, 1965)
• Language ‏ : ‎ English
• Item Weight ‏ : ‎ 4.24 pounds
• #487 in Decision-Making & Problem Solving

About the author

Richard rusczyk.

Richard Rusczyk founded Art of Problem Solving (AoPS) in 2003 to create interactive educational opportunities for avid math students. Richard is one of the co-authors of the Art of Problem Solving classic textbooks, author of Art of Problem Solving's Introduction to Algebra, Introduction to Geometry, and Precalculus textbooks, co-author of Art of Problem Solving's Intermediate Algebra and Prealgebra, one of the co-creators of the Mandelbrot Competition, and a past Director of the USA Mathematical Talent Search. He was a participant in National MATHCOUNTS, a three-time participant in the Math Olympiad Summer Program, and a USA Mathematical Olympiad winner (1989). He graduated from Princeton University in 1993, and worked as a bond trader for D.E. Shaw & Company for four years. AoPS marks Richard's return to his vocation: educating motivated students.

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Customers find the writing quality well-written, interesting, and thought-provoking. They also say the concepts are useful for both classroom and self-study, and essential for geometry.

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I am an Art of Problem Solving Drop-out.

• art of problem solving

By Jenn in Mo , September 21, 2010 in High School and Self-Education Board

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We're a mathy family here, so I'm feeling kind of like a failure here, but I closed the book today and said, "Enough." My math-loving son was diligently struggling through hours of math a day and getting nowhere. It took nearly two months to get through two chapters and I know he couldn't pass any review tests. He understands algebra, but this is....different. My husband and I are struggling to understand half of the problems ourselves...and this is our *thing*, ya know?

I haven't heard a negative word about AoPS yet, so it's kind of embarrassing to admit, but I just do not "get" some of these questions. Anyone that gets it feel like helping to clear the mud on this one?

2.38 What number must be in the blank in the expression 3(x+7)-_(2x+9) if the expression is the same for all values of x?

The solution manual says that "if the expression is the same for all values of x, then the x's in 3(x+7) must cancel out with those in _(2x+9).

My question is...WHY must they cancel out? It's a random, unfinished number sentence. What is in the original problem that tells me they must cancel? What am I missing here? Knowing they must cancel, we can work the problem, but I'm not grasping why I should know they cancel each other out. :svengo:

My other question is, what do I do with this book now? Do I take him through NEM and then come back to this or avoid it forever? I've never given up on a program before. I chose it because the other algebra books were too easy. We've ran into hard things in other books before, but stopped and worked through and moved on. Every day I see him patiently ramming his head into the AoPS wall and it's not something I can help him just "work through" this time. Even though I know that, I still hear Frankie Avalon in my head singing AoPS Drop-Out. :blush:

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2.38 What number must be in the blank in the expression 3(x+7)-_(2x+9) if the expression is the same for all values of x?   The solution manual says that "if the expression is the same for all values of x, then the x's in 3(x+7) must cancel out with those in _(2x+9).   My question is...WHY must they cancel out? It's a random, unfinished number sentence. What is in the original problem that tells me they must cancel? What am I missing here? Knowing they must cancel, we can work the problem, but I'm not grasping why I should know they cancel each other out. :svengo:   My other question is, what do I do with this book now? Do I take him through NEM and then come back to this or avoid it forever? I've never given up on a program before. I chose it because the other algebra books were too easy. We've ran into hard things in other books before, but stopped and worked through and moved on. Every day I see him patiently ramming his head into the AoPS wall and it's not something I can help him just "work through" this time. Even though I know that, I still hear Frankie Avalon in my head singing AoPS Drop-Out. :blush:

(Okay LOL on the Frankie Avalon - I love that song!)

But if the value of the expression is the same for all values of x, that means there won't be any x's left when you simplify it. Otherwise the value of the expression would change for each different possible x.

Have you considered the classes? I know it's a lot of money for a maybe (although I think you have three weeks to bail and get a refund) but I find that there are things I should know but can't always blurt out right when DS needs them... and I like the idea of having someone else who is prepared to do it and other kids who can add to the discussion. Even one math jam left me going "wow - this guy rocks"... :) DS is starting two AoPS classes this year, so I'm not really speaking from experience yet, but I know I'd be stuck going "uhhhhhh...." even on things I really should be able to get. It is hard stuff, and not the "I can teach this in my sleep" of other algebra and geometry programs. I've tutored those for years, but AoPS really is quite a bit more.

8filltheheart

Well, I was in a serious minority (a group of 1, me ;) ) on the k8 board when a mom asked about AoPS for a slow, methodical avg student and I said I would not recommend it. Everyone else was saying that they were accessible to all students.

I have a lot of good math students (I had 1 take alg in 5th, 1 in 6th grade, and 3 others in 7th), but I only have 1 child that I would use AoPS with. He is not just good at math; he is passionate about math. He lives and breathes math. He has taken several AoPS classes and they are tough. He spent hours this summer on their alg 3 challenge sets. Thing is........he wants the challenge. That sort assignment literally makes him smile and jump right in.

My other kids do not desire that type of math depth. They used/are using programs like Foerster. I do not think they are being deprived at all. My ds that loves AoPS thinks mathematically and sees the world that way. The others are just good at math. :)

FWIW......I don't think you have anything to be ashamed of. The books are designed for the top 2-3% of all math students (not all students). They just aren't for everyone. (I couldn't teach them if I tried. He either takes their online classes or has a math coach for them. They are wayyyyyyyyyy beyond my abilities and my dh's as well (and he is an engineer! ;) )

ETA: Thought I should share that if I had known about AoPS umpteen yrs ago, I would have wanted my oldest to try them. I do think they stretch mathematical comprehension beyond the norm......basing that on the fact that my 14 yos now talks some strange language that I don't have a clue about what he is saying. All that said, I **know** that the rest of my older kids would say no way. (as a matter of fact my 11th and 6th graders did!! )

Guest Cheryl in SoCal

Well, I was in a serious minority (a group of 1, me ;) ) on the k8 board when a mom asked about AoPS for a slow, methodical avg student and I said I would not recommend it. Everyone else was saying that they were accessible to all students.   I have a lot of good math students (I had 1 take alg in 5th, 1 in 6th grade, and 3 others in 7th), but I only have 1 child that I would use AoPS with. He is not just good at math; he is passionate about math. He lives and breathes math. He has taken several AoPS classes and they are tough. He spent hours this summer on their alg 3 challenge sets. Thing is........he wants the challenge. That sort assignment literally makes him smile and jump right in.   My other kids do not desire that type of math depth. They used/are using programs like Foerster. I do not think they are being deprived at all. My ds that loves AoPS thinks mathematically and sees the world that way. The others are just good at math. :)   FWIW......I don't think you have anything to be ashamed of. The books are designed for the top 2-3% of all math students (not all students). They just aren't for everyone. (I couldn't teach them if I tried. He either takes their online classes or has a math coach for them. They are wayyyyyyyyyy beyond my abilities and my dh's as well (and he is an engineer! ;) )

:iagree:I haven't used it yet but have been looking through the Intro to Counting and Probability and a bit of the Intro to Algebra and from what I have seen I wholeheartedly agree. No math curricula is the answer for every student but IMHO AoPS is going to be a good fit for the minority of students. One of my ds's would DIE if I had him use AoPS and another I think will like it because he thinks that way, though we'll only know after we try it.

I had a look at the algebra and geometry and found the layout visually confusing, which is kind of weird since in some ways it is not as busy or distracting as textbooks in general. But it is packed solid, and hard to read as a text, if that makes any sense. And algebra is my own strength. My dd went for Discovering Algebra instead.

The geometry book struck me similarly as user-unfriendly, but that may be again just my visual reaction to such a dense text.

However, that similar packing did not bother dd with the data and probability books, which she greatly enjoys. So maybe it depends on the kid (and grown-up) as well as on the area of math involved.

(Okay LOL on the Frankie Avalon - I love that song!)   But if the value of the expression is the same for all values of x, that means there won't be any x's left when you simplify it. Otherwise the value of the expression would change for each different possible x.

Ha! Lightbulb! Thank you! Regardless of what x is, the expression will equal the same thing. You're speaking my language. The book is not. :tongue_smilie:

I am relieved to hear these responses. He loves math and enjoys a challenge, but I couldn't at all say that he is passionate about math. I had forgotten that Foerster was on my list of maybes before I heard that AoPS was the crème de la crème of algebra texts. So....NEM or Foerster....thoughts?

I know absolutely nothing about NEM, so I can't offer any insight there. I have used Foerster with all of my older kids, including my ds that now uses AoPS. He used Foerster for both alg 1 and alg 2. His first AoPS courses were Intro to Counting and Prob and their alg 3 courses online and he owns several of their other "off normal track" math books that he works through on his own.

My oldest used Foerster and it more than prepared him for university level cal and an engineering major.

I'm not sure I can explain the differences very easily. Foerster is a solid math program and they absolutely learn the math skills they need to perform high level math problems, etc. No question.

AoPS helps them process math in a completely different fashion. Ds goes around "discovering" concepts and "proving" things like why x equals some bizarre thing or how an indefinite number of fractions add.......I don't know......I just nod my head!!! :lol: He thinks he wants to double major in astrophysics and math. For him it is a match. I have only ever met 2 other people that think that way.......one is now majoring in math and the other has a phD in math. For the rest of mere mortals, I think we are fine w/o it!

In The Great White North

Dc used/are using Foerster. They arde very solid math books. I have the AoPS Problem Solving, Counting & Probability and Number Theory books. Dc don't like them. They are not straight forward. Dc like to have an example, an explanation and get the problems done. Foerster does this for them. AoPS does not.

AoPS is for people who like to PLAY with their math. If your idea of a great time is to go round and round with a math problem til you figure it out, AoPS is for you. Yes, the top 2-3% of math students in the country are more likely to enjoy that, but even they don't always like that.

I've seen but not used Foerster, so I can't compare... but NEM is good challenging work. Most of it is more straightforward than AoPS (examples first, exercises second) but there are Challenge sections and Mathematical Investigations that could be frustrating in the same ways AoPS can be. They do (in those sections) throw you in and expect you to dig yourself out. And to some extent they leave some gaps in the regular explanations too -- nothing huge, but enough that sometimes the student (or the teacher) has to connect the dots.

C_l_e_0..Q_c

I'm in the opposite situation. We're a NEM drop-out. I'm so much happier as a mom with AoPS *and* the online class. Someone else is teaching math to my math kid!

(and I"m good at math too, I did math all the way to a Master's level, although it was not my major - I'm an engineer, we need math )

My son is truly having a blast with the online class. He did Algebra 1 over the summer. The kids at the summer pool who learned he was doing a math class assumed it was remedial, until they saw a problem! LOL. Sweet nerd revenge. :)

The math classes are totally worth the cost. Plus they force the kids to move forward, and not spend 2 months on 2 chapters. In 15 weeks, they did 14 chapters (possibly 13, I'm not sure) so the interest is kept high.

at the beach

I agree that AoPS is for people who enjoy playing around with math. I think I am one of those who said something along the lines that more people can be successful with it than the top few percent. But I think I also said that sometimes the solutions/explanations gloss over things or skip a step, assuming readers will see that step in the problem when they might not. I felt it could be used by more than just the top few percent because I think that kids often underestimate their abilities. I also agree with the pp that even kids in the top few percent who can do it may not want to do it because it does take a lot of time and puzzling.

I was terrified of math from 8th grade on. I never took math in college but took logic to avoid it. When I signed my daughter up for AoPS this summer, I decided to give the book a try. I did the first three chapters. I wanted to help my daughter if she needed it, but she was the one helping me :001_huh: and the class moved so fast that I couldn't keep up.

The problem that you mention, to me, looks like it is asking you to make the 2x the same as the 3x so the only thing that works is 3/2. How do you know it will cancel? I think you know that because it's a subtraction problem. Maybe I am oversimplifying this.

Maura in NY

NEM is an integrated program - Algebra/Geometry/Trig and rolled together. It's challenging, in a good way, but it doesn't fit the typical Algebra/Geometry/Algebra II/Trig-PreCalc/Calc track.

FWIW, my ds used NEM 1 in 7th, thinking he would stick with it for 4 years. Instead, we switched. He didn't use Foerster's Algebra I, but he did use Foerster for Algebra II and PreCalc. Great real world application problems.

We used AoPS for several months and also found some of the problems strangely worded. But, our biggest problem with AoPS was not enough repetition.

We are using Foerester's Algebra now. It has more than enough problems for us, but it's much easier to eliminate problems than try to add more in.

Miss Marple

Not a drop-out yet, but we are doing AoPS very slowly and I've added NEM2 back as the primary math. Ds is still working through the geometry book (45 minutes per day), but we've put the algebra book away because he already did LOF Beginning Algebra and the NEM should cover the bases thoroughly.

I'm finding that hormones cause my son to be less inquisitive and less dedicated right now. He does great with math, so I chose the other program I love - Singapore NEM, and it is going very well.

If we never finish the AoPS books that will be OK because NEM is the primary curriculum (which we will finish). I know that any exposure ds has had with AoPS has helped fine tune his mathematical abilities.

Well, I was in a serious minority (a group of 1, me ) on the k8 board when a mom asked about AoPS for a slow, methodical avg student and I said I would not recommend it

:iagree: I cannot imagine how frustrated a student and a parent would be trying to work through this program and thinking that it is accessible for all students!

The problems in NEM can be plenty challenging at times. My son did NEM 1 before switching to AoPS.

Regarding AoPS Algebra 1, they introduce Algebra 2 concepts, too. That doesn't make it easier! Ds thought the middle of the text was difficult and often trudged through the problems, but then he flew through the last few chapters. He thought they were easier, even many of the challengers. I don't know if they really were, or if he just started to get the hang of the text and problems.

When it comes to math, it's so important to pick what works and then bite off and chew well at a pace that's suitable for the student. I wouldn't hesitate to step back and reconsider if something wasn't working.

  AoPS is for people who like to PLAY with their math. If your idea of a great time is to go round and round with a math problem til you figure it out, AoPS is for you. Yes, the top 2-3% of math students in the country are more likely to enjoy that, but even they don't always like that.

I agree entirely with the bolded.

If anybody is deciding whether to go with the AoPS classes, there's a Math Jam on the subject this afternoon/evening (7:30 Eastern, I believe). It will include sample questions from the class, so you can try them out.

Math Jams are free informational sessions, usually hosted by Richard Rusczyk, who is always responsive to questions. If he can't answer your question within the confines of the session, he'll likely invite you to e-mail him and he'll help you decide whether a class is right for your family.

We're mathy. . . and we're AoPS drop outs as well.

Dd & I tried Number Theory for a couple/few months. It actually went OK so long as *I* worked through *every section* and *every problem* on my own before dd tried it (or simultaneously sitting together).

The exploration and problem solving was interesting. I rather enjoyed it. But, I just *don't have time* to do it right now.

We dropped it after a few chapters -- which were successful but slow b/c I just couldn't make myself find the time to do it often enough to keep up w/ dd's needed pace.

So sad. . .

Now y'all are scaring me. My dd loved the AoPS Number Theory book so much this summer, I bought Alg I for her (but we don't start for another year...) I had been planning on Foerster's, so I've got both ready to go (well, I still need that pesky Foerster's Solutions manual...)

We're mathy. . . and we're AoPS drop outs as well.   Dd & I tried Number Theory for a couple/few months. It actually went OK so long as *I* worked through *every section* and *every problem* on my own before dd tried it (or simultaneously sitting together).

Dd and I worked through all the examples together, but then she did the problem sets pretty much on her own (except I let her skip the challenge problems at the end of the chapters). Was your dd just needing you to sit with her for the "lesson" part, or also the problem sets? I didn't mind working through the lesson with her... I actually learned a lot myself and had fun... :tongue_smilie: For some reason I really like the layout and presentation of these books... OTOH the Lial's layout really drove me crazy when I first saw it (I'm getting used to it now that my other dd's working through BCM).

But now you guys are intimidating me a bit... :001_huh: I do think the Algebra text looks more challenging than the Number Theory, but I'm hoping after she's gotten through Singapore DM1, she'll be preparerd (or I guess we'll do Foerster's after all...)

I found the solutions manual for Foerster this afternoon! I finally called the publisher and it turns out that they renamed the book and it is now called Classic Edition instead of Foerster's. The ISBN # is 0201861003. I can't find it used anywhere, but it is available new at pearsonschool.com.

I'm still torn though. I loved Singapore so well and would like to try going on with NEM. But I don't want to commit to it being his math for all of high school. I hear that Foerster does an excellent job with proofs, which I think are important. I may end of tossing a coin before this is over.

This is exactly what I was trying to express in the other thread! It's just as much about the approach as the difficulty, imo. Yes, you need to be a good math student, but I dont' think you need to be a TOP math student. Not in the sense of the top 2% to 3%, at any rate. I can't imagine my dd would score anywhere near that high, but she loves AoPS.

And you can be a top math student, but if you hate this approach, it will be very hard to persevere and succeed.

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Math Courses: Advanced Math, Taught Virtually

AoPS Academy offers small, engaging virtual math courses year-round for motivated students in grades 2 through 12.

In instructor-led classes, your student will develop problem-solving and communication skills that will help them succeed in school and beyond. An interactive online platform complements live instruction from mathematics experts.

Students learn from live instructors in an interactive virtual classroom. With 10 to 16 students per class, there’s plenty of opportunity for direct interaction as students collaborate with their class and dedicated peer group.

All of our courses follow a curriculum designed by AoPS. Since 1993, AoPS has trained the next generation of resilient, confident problem solvers. We believe in tough but accessible challenges and student ownership of learning.

Our Honors Math courses 2–5 use Beast Academy, a rigorous math curriculum designed by AoPS. Beast Academy is set up as a complete math program, but it can also be used as a supplementary curriculum in a public, private, or homeschool setting.

Starting at Level 6, we offer two parallel curricular tracks. While our Honors Math courses continue to challenge students to develop their critical thinking skills, our Contest Math courses add problem-solving sessions to prepare students for math competitions like MATHCOUNTS, MAA AMC, and more.

The AoPS curriculum team has designed a wide variety of special activities and explorations for our summer courses. These classes dive into topics that we believe are essential for students' success in the following academic year and introduce students to mathematical concepts not typically covered in a school curriculum.

Requirements

Classes are held through video conferences in an online classroom. Students will need:

• Access to a desktop or laptop with a camera and microphone
• A calm, quiet location to work

A higher-level course is built upon the knowledge and skills of a lower-level course. We recommend first honing in on your student’s level by their age, and then have them take a placement test .

Math Courses

Academic Subject

Grade Level

Summer Math

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Degree (geometry)

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The number 360 as the amount of degrees in a circle was probably adopted because it approximates the number of days in a year.

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