Looking for geometers

[kiana]

Out of all the topics, this is the one that I never took a class in after high school. I have little familiarity in what's covered in the standard high school syllabus. But I know we have some experienced educators out there and someone has to have taken a second class in geometry. 

 

I'm looking for the (proof-oriented) book that made you sit back and notice how awesome geometry was. Ideally aimed at a second class in geometry, but if it were something that could be done as a first course by a motivated/talented student, that'd be fine too. 

 

Thanks. 

[regentrude]

Art of Problem Solving, Introduction to Geometry

proof based, awesome, can be taken as first course for motivated student or as second class after basic intro

I've worked through it twice, with two kids. Beautiful problems, beautiful proofs, and some as hard on the second try three years after the first ;)

[Kathy in Richmond]

Yes, AoPS Intro to Geometry goes above and beyond other intro books and is fully proof based. It's easily in the '2nd course in geometry' category; I tutor honors high school geometry locally, and AoPS is just at another level altogether. It's lots of fun for me. One of my goals this year is to work through all the challenge problems...not an easy feat, but totally enjoyable for this math nerd!

 

After AoPS, these are my favorites at the next levels of difficulty:

 

Plane Euclidean Geometry: Theory and Problems by AD Gardiner and CJ Bradley

 

Challenging Problems in Geometry by Posamentier and Salkind (Dover paperback)

 

Geometry Revisited by Coxeter and Greitzer

 

[kiana]

Yes, AoPS Intro to Geometry goes above and beyond other intro books and is fully proof based. It's easily in the '2nd course in geometry' category; I tutor honors high school geometry locally, and AoPS is just at another level altogether. It's lots of fun for me. One of my goals this year is to work through all the challenge problems...not an easy feat, but totally enjoyable for this math nerd!

 

After AoPS, these are my favorites at the next levels of difficulty:

 

Plane Euclidean Geometry: Theory and Problems by AD Gardiner and CJ Bradley

 

Challenging Problems in Geometry by Posamentier and Salkind (Dover paperback)

 

Geometry Revisited by Coxeter and Greitzer

 

Have you ever seen Moise "Elementary Geometry from an Advanced Standpoint" in person? I know the high school version used to be highly recommended on these boards prior to AOPS becoming popular, and it *looks* very interesting. I don't see a version under $40, though. 

Edited January 9, 2018 by kiana

[Kathy in Richmond]

Have you ever seen Moise "Elementary Geometry from an Advanced Standpoint" in person? I know the high school version used to be highly recommended on these boards prior to AOPS becoming popular, and it *looks* very interesting. I don't see a version under $40, though. 

 

No, I haven't seen Moise in person. I did find several cheaper used copies on Abe Books, though (Amazon was much pricier).

 

[lewelma]

After AoPS Geometry, DS did the UKMT Plane Euclidian Geometry text that Kathy listed. It took him about 2 months.  Then he took the Olympiad Geometry class (3 months, it unfortunately does not have a textbook).  Together these definitely constituted a second year of Geometry. (The class was very hard for him at the time).

 

DS now is working through Problem Solving Tactics from the Australian Math Trust.  It includes all 4 streams of Olympiad math, so is 1/4 geometry. 

 

http://www.amtt.com.au/Products.php?Operation=SetSessionVariable&Variable[ProductCodeID]=PST&Variable[PrevPage]=http%3A//www.amtt.com.au/

 

Ruth in NZ

Edited January 10, 2018 by lewelma

[domesticidyll]

Writing teacher here, not a geometer, but I'd say a big part of the learning my DS is getting from AoPS geometry is the writing out of formal paragraph style proofs. I have him start with goal and strategy, thinking through what is hard about a particular problem, how to summarize the approach in a few words, maybe mention what tricky concept is being explored. The writing piece had been challenging, harder than the math sometimes, but thinking through how to present something has helped him appreciate how pretty some of the problems are.

[lewelma]

Interestingly, ds learned to write for English class by writing math proofs for AoPS.  He went from an low-end 8th grade writer to a high-level 11th grade writer in 1.5 years by writing 4 long AoPS math proofs each week. He did not write a single English paper during those 1.5 years, but instead took Olympiad geometry, Intermediate combinatorics, Intermediate Algebra, and PreCalculus classes through AoPS.  The markers were tough and didn't let his English slide. They marked for organization, grammar, and proof reading.

 

Writing is thinking made clear.  When ds could write a clear, well-reasoned math proof, it was an easy jump to writing clear, well-reasoned English papers.

 

Ruth in NZ

[kiana]

Interestingly, ds learned to write for English class by writing math proofs for AoPS.  He went from an low-end 8th grade writer to a high-level 11th grade writer in 1.5 years by writing 4 long AoPS math proofs each week. He did not write a single English paper during those 1.5 years, but instead took Olympiad geometry, Intermediate combinatorics, Intermediate Algebra, and PreCalculus classes through AoPS.  The markers were tough and didn't let his English slide. They marked for organization, grammar, and proof reading.

 

Writing is thinking made clear.  When ds could write a clear, well-reasoned math proof, it was an easy jump to writing clear, well-reasoned English papers.

 

Ruth in NZ

 

Interestingly, some of my students in proof-based classes have said "I learned a lot more about grammar/writing a clearly structured argument in this class than I did in freshman comp".