5 comments about Pre-Algebra Demystified.

1. "Demystified" is more like "profoundly confusing." It's just another book rushing through problems with little or no explanation. It really angers me that there are so many books like this that promise enlightenment but provide headache. Maybe it'll work for you, but if you're like me and REALLY need this stuff taught SLOWLY step-by-step (meaning no steps skipped), then try another book. Upon reading this book, I felt as though it assumed I had experience in the subject it was supposed to introduce me to. Try Painless Algebra by Lynette Long-while not flawless, it is the best I have used thus far and has brought me, a math loser, into the game.



2. Although the DeMystified series promises to demystify math, it helped me in some areas;however, with this particular title I found the book seriously weak on practice problems. I bought it in order to brush up on my basic math skills, but in my experience with it, it wasn't enough to throw out five or ten practice problems per section and assume that I'd know the concepts well. Some, like me, need to be able to practice quite a few problems to get the idea or just to be sure that I understand the math concept correctly. I found this to be the books greatest weakness.
   
   One would do better to just study from their class texts since these works often do give you the practice and detailed explanation you may need. If one is looking to cram (shame on you), then this book may work. However, then again, it may not since there are so few practice problems.



3. HAHA! Ok, I'll explain why I am laughing. I have been working on this book and everything has been good until chapter 11 page 211. I remembered when I first bought this book, I read this comment and thought "ok the guy (S.Brown) just doesn't know how to answer the problem" I came on here looking for this comment to see if it was the same comment I had. That is why I am laughing. The author really does just give up after chapter 10! Although there are a few errors in this book, it's a pretty ok book. Considering I didn't even know my multiplication table before I started this book and now I can pass math tests easily. Yah! Except the graphing. Luckily I have three other math books that can help with this.



4. I bought this book (and a bunch of others) because I wanted to prepare myself for a college math assessment test and score high enough that I could jump straight into statistics (I know, pretty ambitious!).
   
   My current situation?
   
   1) I haven't studied algebra (or any math at all for that matter!) in about 20 years
   
   2) I didn't learn math in English
   
   So, after opening the first algebra book and realizing I didn't remember how to do even more basic operations, like dividing large numbers by large numbers, I decided I needed to get something that went even further back.
   
   I bought about 10 books, thinking that it was a good investment, as skipping the basic math classes at about $300, plus the cost of books, for each, would save me quite a bit of money.
   
   After reading about 40 pages of the first basic math book, I was very disappointed. It was unclear, complicated and just didn't make much sense to me. I started to wonder if things had changed THAT much since I used to study. I put the book aside and pulled this one from the pile. Well, it has 12 chapters and I have completed 8 so far. The book is great! I read some bad reviews and, who knows, maybe chapters 9, 10, 11, and 12 are rubbish... But I doubt it!
   
   The approach is logical, practical and easy to follow. There are quite a few exercises and tests at the end of each chapter, as well as a complete test at the end of the book. I usually complete a couple of chapters, then take all the chapter-end tests from the previous chapters again before proceeding. This way, the information stays fresh in my mind.
   
   I liked this book so much that I bought about 4 or 5 more books from the DeMystified collection, including Algebra and Math Word Problems (the latter by the same author). Ok, so maybe I buy books compulsively at times, but I am very excited about math, probably for the first time in my life.
   
   If you need to take a refresher course, or if you need support for classes you are taking, I truly recommend this book!
   
   Good luck!



5. Thank you, Mr. Bluman. You have cracked into my brain, and now I can do math, without a calculator, without feeling like my head will explode! Mr. Bluman is a gifted, no-nonsense teacher who can teach anyone math with this straightforward, brilliantly crafted self-teaching manual. He even tackles math phobia -it is real- and dispatches it effectively with tips to get yourself going every day. This book should be in every junior high and high school library. He gives you the tools and then with practice, you can solve the problems. The format of explanations step-by-step, repetition, practice, and practice tests and final tests in every chapter is an excellent approach to truly "getting it". Thanks a million!

No comments about Trigonometry (9th Edition).

5 comments about Counterexamples in Topology.

1. As a graduate I encountered a book called "counter examples in analysis" which I found very useful. I always dreamed of such a book in topology, this book exceeds my dreams. It is great. It does not cover all the examples that I have used over the decades but it does cover some that I have never seen. The style is quite readable for a professional topologist. The book goes into a lot of interesting details (and some while not interesting to me would be another person). In short for me it is an essential book. The question is to whom else would this be interesting to. It is clearly of little use to a first year student and less to more advanced student. It's brand of topology is not the current cutting edge. So the audience for this book is limited to a small group and for these people it is top notch.



2. This book has examples in it that are "missing", so to speak, from many regular topology books. It aims to shore up some of these shortcomings, with examples that the student can see and understand. There are charts and graphs, as well as a detailed explanation. Some "problems" often found in regular topology books are solved. Very few proofs, if any, are given. This is not a book meant to be studied without a regular textbook on topology, only to be used as an overall review of problems and short basic premises of topology. Use this in addition to your regular fare, but keep it close at hand when doing homework or preparing for an exam.
   There are fundamentals on Cantor's Theorem, the countability or uncountability of sets, compactness, closed and bounded functions, open sets, continuity, connectedness, etc. All these are basic to topology, and this book does address them, but in a brief way. It then shows a basic overview of topology that helps greatly to understand the different fields of topology.



3. A distinct characteristic of point set topology is that it builds on counterexamples. If you thumb through any PST text, many theorems are in the form "If the space T is A,B,C, then the space is X,Y,Z". The point of point set topology (pun unintended) is too determine what A,B,C are, and to weaken the hypothesis. "Can we take condition B out? Maybe hypothesis C can be weaken considerably?" How can we answer these questions? You're right, by counterexamples. Students who want to master point set topology should know the various counterexamples, no matter how contrived or unnatural they seem. While textbooks usually present a counterexample to show why Theorem Three Point Five Oh will not work on a weaker assumption -- most students (and teachers) tend to skip these parts. A collection of counterexamples presented in this book (excellent organisation, by the way) is an essential supplement of a topology course; it enables one to 'see' between the points, so to speak.



4. To paraphrase Chandrasekhar's review of Watson's Bessel functions text, this is "a veritable mine of information... indispensable to those who have occasion to use point-set topology." I don't think this book is intended to be a text (& I think the authors say so), in which case it would be terrible because it doesn't explain the concepts very much. It's mostly a catalogue of every kind of set you can come up with, every kind of topology you can put on it, and what properties it has such as what T_i axioms the space satisfies, whether it's compact, para compact, etc etc. Most of the time such things are proven, but be prepared to think hard sometimes about the proofs or fill in details. I'm the kind of student where I have trouble understanding things which are highly 'counter-intuitive' so I had trouble proving things, even when I knew definitions, when I did topology for the first time last term. Once I saw this book though I got used to all the weird things in topology (like the ordered square, R in the lower-limit topology, Sorgenfrey plane, etc etc). This book is incredibly useful as a reference.



5. I have found this book to be confusing to use and therefore of little to no value. If I had seen in a bookstore and not Online I would not have purchased it. I also purchased Schaum's Outline of General Topology which is very good.

5 comments about Sacred Geometry: Deciphering the Code.

1. This book is well-written, gorgeous, printed on fine paper with extraordinary illustrations. It introduces sacred geomentry in art, architecture, nature, and the history of science. A fine text for a layperson with acalculia! Obviously to learn more about a particular application of sacred geometry would require additional books that focus on the reader's area/s of interest.



2. Although this may not be relevant to most people, this is a very pretty book. Two things attracted me to it initially: The title and the cover, in that order. The title interested me because of a class my girlfriend took about sacred geometry, including the meanings of the shapes and the colors. The cover interested me becaue of the ammonite shell on the cover. I first noticed the ammonite in Alberta, Canada when a shop vendor explained the critter to me. They are older than dirt and the shells have varying degrees of opalescence that are just mind-boggling to me. Anyway, back to pretty: unlike most books, the inside of this book is loaded with pretty colors, diagrams, and colored pictures. There are 152 pages of information plus 8 more of bibliography and index.
   
   Now for substance: the book bigins with some introductory information on geometry, why it is considered "sacred," how geometry was often used to situate churches/temples in history, and in the architecture of such places, the history of geometry, including the embodiment of numbers in music and measurement, and Pythagoras and his investigation of the sacred and mystical properties of numbers.
   
   The book continues with generally 2 pages on each of many mathmatical and geometry related subject matter, such as: fractals, crystal structure, replicating geometric patters in plant and animal life, the structure of snowflakes, genetics and the DNA double helix structure, Alfred Watkins and the ley lines, Stonehenge, crop circles, the structure of the Temple of Solomon, geometry in art, geometry in several cathedrals, etc.
   
   By the way, if you have ever wondered how much a cubit measures, it was originally used to indicate the measurement of the fingertip to the elbow, but was later standardized at 17.674 inches.
   
   I find this a very interesting book. It's got a lot of little bits of information about a lot of different but related topics, related in math of course. And it's even pretty.



3. This is an incredible resource for anyone interested in the architecture of the universe and the magic of mathematics. It is indispensable! It inspires the mind to view consciousness from the eyes of creation and evolution. If you like this subject, visit:
   http:// www.alexplays.com



4. /
   
   Sacred Geometry by Stephen Skinner
   
   This is the best of all the books on the subject. The extant texts were becoming dated and a new book was long overdue.
   
   It consists of 160 pages, and about 1/5 to 1/3 of each and every page is illustrated, and most are color illustrations. The author devotes about 2 to 5 pages to each subject. The author indicates that GEOMETRY is considered sacred because it shows the ARCHETYPAL patterning of things. This carries over into the realms of Architecture, Mathematics, Conceptual Abstractions and of course, NATURE.
   
   The author begins with the Greeks of course, and continues on into the Middle Ages, where the basic curriculum for study was the TRIVIUM (three subjects): LOGIC, GRAMMAR, and RHETORIC.
   
   These subjects expanded into the QUADRIVIUM, which added GEOMETRY to LOGIC, GRAMMAR, and RHETORIC. By page 22, the author gives consideration to MUSIC, VIBRATION and WHOLE NUMBERS. Those 2 pages are followed by FRACTIONS.
   
   By page 26 (the number of LOVE and the NAME OF GOD in Gematria, the author introduces a favorite of many, ERATOSTHENES, the "man who measured the earth".
   
   Egypt and early measurement follows, and then PRIME NUMBERS, and this chapter delightfully includes a very important graph for us all, the SIEVE OF ERATOSTHENES, by which Primes are discovered.
   
   By page 34 the author introduces the GOLDEN MEAN, and this section includes the FIBONACCI SEQUENCE.
   
   The author reserves in depth discussion of EUCLID until page 40, and by page 44, moves into THREE KEY TRIANGLES, the Equilateral (three equal sides), the Right (90 angle at base) and the Isosceles (whatever the heck that is! NO, just kidding. Two equal sides!)
   
   Page 46 shows three ancient geometrical problems:
   (1) Squaring the Circle, (2) Doubling a Cube, and (3) Trisecting an Angle.
   
   Page 48 covers CURVES & LOGARITHMIC SPIRALS, and by page 52 consideration is given to GEOMETRY OF IRRATIONAL NUMBERS. Page 54 covers THE FIVE PLATONIC SOLIDS. Page 56 covers the THIRTEEN ARCHIMEDEAN SOLIDS. The lucid color illustrations on these pages are fantastic, each solid being shown in vibrant yellow, orange, green and red.
   
   Page 58 covers the FRACTALS, and page 61 shifts into the GEOMETRY OF NATURE, including PLANT GROWTH, CRYSTAL STRUCTURE, LIVING SPIRALS, LIVING WATER, SNOWFLAKE WONDERLAND, GEOMETRY OF GENETICS etc.
   
   Page 75 introduces GEOMETRY IN ASTRONOMY and COSMOLOGY and ends in Significant Sky Markers. Then comes MAPPING the WORLD and LATTITUDE & LONGITUDE. MEASURING TIME BY SUN & MOON is on page 84. Then the HIDDEN CONNECTION BETWEEN TIME & LENGTH.
   
   By page 89 we are shown THE GEOMETRY OF THE MANMADE WORLD, SACRED GEOMETRY & THE LANDSCAPE which covers some material on Alchemist John Dee and sites such as Glastonbury, etc and other sites. Page 202 covers ASTRO-ARCHAEOLOGY, a favorite subject of many, and covers other English sites, and finally STONEHENGE.
   
   I was surprised by the next informative subject, because I've been thinking a lot about the nature of life and how the LABYRINTH relates to human experience. Page 112 covers LABYRINTHS & MAZES.
   
   CROP CIRCLES comes on page 114, and I am happy to say that none of that nonsense about the cause of crop circles being two pranksters with some boards is included in Stephen Skinner's book.
   
   Page 116 introduces SACRED GEOMETRY IN ARCHITECTURE, and this covers PYRAMIDS.
   
   By page 120, we are introduced to the SECRETS OF HERODOTUS, of which I knew nothing. Then the TEMPLE OF SOLOMON is covered and the Dome of the Rock.
   
   By page 124, we find the PARTHENON, a favorite of mine because I saw it, and must tell you that when you see it, you can be mightily impressed with the powerful beauty of ancient architecture.
   
   Another surprise comes on page 128, with Leonardo Da Vinci and the ARCHITECTURE OF MAN.
   
   On page 130 comes CHRISTIANITY AND THE SACRED FEMININE, which covers the "vesica piscis" which is the common intersection area of two circles. Then the MILAN CATHEDRAL, CHARTRES CATHEDRAL, ST. PAUL's CATHEDRAL, and finally MODERN ORGANIC ARCHITECTURE.
   
   Then we come to SACRED GEOMETRY IN ART on page 140 and on 141 ROGER BACON and GEOMETRY, LIGHT & OPTICS. Whew!
   
   What would a book on geometry be like without GEOMETRY PERSPECTIVE IN THE SERVICE OF PAINTING? By page 144 we find LUCA PACIOLI and the DIVINE PROPORTION. Finally, Leonardo DaVinci's use of PERSPECTIVE in the painting THE LAST SUPPER. Winding down to page 148, we come to PAINTINGS ANALYZED GEOMETRICALLY. Man, this book is full of fantastic insight into several thousand years of human culture.
   
   Then, at the very end, THE TREASURE OF RENNES-LE-CHATEAU, which I believe featured prominently in the books about "THE DA VINCI CODE" which was made into the popular movie.
   
   This is one WHOOPEE book. Glad I bought mine at first sight. I'll never regret it.--Bruce R. Bain
   
   /



5. I would have given the book more stars, unfortunately the last few sections of the book are too christian for my own tastes. The book is well written and presents the information well, but it does fall apart in the end. With all the material of sacred archeological sites, I dont know why the Author chose to stay within the scope of christian churches, when most people who pick up this book are more intrested in the true sacred.

2 comments about Islamic Design: A Genius for Geometry (Wooden Books).

1. I haven't looked at it in too much detail but it has plenty of cool, trippy looking geometrical patterns. It actually shows you how to make all these patterns as well. Nice.



2. I just recommend, not only about this book, but all the books from this publisher, they are a delight.

5 comments about Sacred Geometry (Wooden Books).

1. This book is a treasure. I was given it as a present and I find myself turning to it for all sorts of ideas and also give it as a present quite regularly. She has managed to pull together a huge amount of wonderful information into a relatively small space. This is an inspiring, beautiful, thought provoking and even useful book. I am a graphic and fabrics designer and I had not come across some of these things before so I am very grateful for them.

   I also really like the way the book is put together, lush textured paper (recycled I note) and quality illustrations. The way the subject is built up stage by stage until we reach the more complex set pieces at the back is very good. It helps you understand the basics of good design, and the use of geometry in this process.

   I think the new-age overtones work very well too. She manages to convey some of the real mystery and magic of the field while never losing sight of the practical purpose of it all.

   Highly recommended.




2. This is a delightful little book.If you have any interest in Geometry,Math,Design,Shapes,Tile patterns,Puzzles,etc.you'll really enjoy this book.Surprisingly ,you can grasp most of this book knowing high school math,;while at the same time those with more math knowledge will also enjoy it as well.I guess it falls right in the realm of Mathematical Recreations.I am amazed that the author has put together a beautifully writen book,including 168 drawings,figures,diagrams and on top of that shows how most are constructed.All this has been accomplished in 64 pages ,including an introduction.



3. This little book, Sacred Geometry, is not only magical and straightforward in its substance, but is a visual delight. It reminds and further inspires to realize the connectedness of all of life and our part in it. It helps me, also, as an artist, to remember the basic forms that resonate in all of creation. This is not only a good book to give as a gift, but is a good one to have on your own bookshelf.



4. This book is only 58 pages long so expect to have read it during breakfast , Im not sure about it, some interesting elements and ideas on tiling and how to draw a dodecagon but as I said its a very short book so is nothing more than a cursory glance , hopefully one day a project with come up where I can use some of the ideas in this book . Its cheap and I guess you get what you pay for , reminds me a bit of a black and white catalouge or something. It could be good for someone who just wants to get a basic cheap idea of what sacred geometry is with a handful of diagrams thrown in , on that front it does deliver but remember 58 pages. less than a time magazine..



5. I had the pleasure of meeting the brilliant and witty author of this book in 2004. :-) This book, like all the Wooden Books series is a gem in and of itself, and combined with others in the series, weaves wonderful contextual insights about the mystical underpinnings of nature, expressed in form, number and dynamic shape. This book has concentrated many useful and fascinating observations about what has become known as sacred geometry into an exquisite little package, with meticulous illustrations. Highly recommended! [...]

5 comments about Discovering Geometry: An Investigative Approach.

1. this book makes you think a lot... you have to figure out like EVERYTHING yourself... there isn't even a glossary... its hard to know if you got the answers right cuz there is no answer key... this book is made for really smart ppl...



2. I've used an older edition of this book in a high school geometry class. While the hands-on approach may be difficult to those who would rather have the concepts told to them, it allowed me to grasp the subject firmly. By allowing students to figure out different concepts, this book truly facilitates learning.



3. This geometry book has thought provoking problems, but that is all that is good about this book. There are many typos and awkward wordings to be found, and even incorrect answers in the teachers edition (my teacher has been correcting answers in his book all year)! This book is also useless without the only conjectures and vocabulary, something that should have been included in an appendix somewhere in this book! If you want to learn geometry, this is not the book to use.



4. Excellent condition. I used least expensive shipping so textbook took a while to arrive.



5. I had the misfortune of learning geometry from this textbook as a student, and now I have the misforture of teaching from it. I remember hating math as a high school student, and textbooks like these were the culprit. In high school, math was always presented as a set of problem-solving techniques that I had to learn and memorize. I was generally able to solve whatever problems came my way, but it always seemed like a trivial and pointless exercise. Luckily, I had some great college professors who made me realize that math was much more than memorizing algorithms, but a comprehensive logical system grounded in deductive reasoning.
   
   Geometry is the only math course in which rigorous deductive reasoning can be made accessible to high school students -- and not surprisingly, it was the first area of mathematics to be axiomatized (by Euclid). Unlike algebra or calculus, almost all of the theorems and formulas in geometry can be systematically obtained from postulates in a way that is intelligible to high school students; on the other hand, I have yet to see an algebra teacher attempt to prove Cramer's Rule or the Binomial Theorem to their students. The fact that geometry introduces students to a different, mathematical way of thinking is the only justification for maintaining geometry as a standalone math course, rather than integrating it into algebra courses. Otherwise, the "facts" of geometry are nothing remarkable in themselves. So what if opposite sides of a parallelogram are congruent? It wouldn't be that difficult to teach students that "fact" in an algebra class when they're learning about slopes of parallel lines. But what's important is that students understand and see how this fact derives systematically from already known facts.
   
   What does all this have to do with the book at hand? "Discovering Geometry" reduces geometry to the same collection of facts and algorithms that students have been doing in every math class since elementary school. While the problems that Michael Serra devises are occasionally interesting and even clever, he completely misses the point of geometry -- to understand WHY those "facts" are true.
   
   Unlike many critics of this book, I do not have any inherent qualms with the investigative approach to learning geometry. Investigation plays a central role in mathematics, and I applaud the author for giving inductive reasoning its fair shake in this book. But investigation has become more of an ideology than a pedagogical tool in this book. Even my weakest students groan at having to do some of the investigations, whose results they deem obvious. There are simply too many unnecessary investigations, many of which exist only to aggrandize the author's educational philosophy.
   
   As a student, I used the second edition of this book. The author has clearly made significant improvements for the third edition, but there are still serious pedagogical flaws. While Chapter 13 is a valiant attempt at introducing students to the deductive method of geometry, it is too little, too late. High school math classes rarely reach the last chapter, and separating the proofs from the theorems themselves feels artificial and contrived. The author makes another questionable pedagogical decision to area and volume into nonconsecutive chapters, Ch. 8 and 10 -- just so he can prove the Pythagorean Theorem using area in Ch. 9. But if he would only introduce similarity before the Pythagorean Theorem, he would be able to prove the Pythagorean Theorem using similar triangles in a much more elegant and motivated way.
   
   The unorthodox ordering of topics to which I have previously alluded creates problems for even the author. There are many practice problems that require concepts or techniques from later chapters. For example, students are asked to construct a square in Chapter 3 given a diagonal, before either the properties of quadrilaterals (Ch. 5) -- or even the properties of triangles (Ch. 4) -- have been introduced! How students are supposed to "guess" that the diagonal of a square bisects the angles -- I do not know. Furthermore, the first proof in the text is a paragraph proof that the perpendicular bisectors of a triangle are concurrent. I can only imagine the horrified looks on the faces of Serra's students. And these are supposedly students who are having too much trouble with the two-column proofs!
   
   There are outright mistakes in the textbook as well besides the usual typos. On page 333, Serra defines an irrational number as a number whose "decimal form never ends" and a transcendental number as a number whose "pattern of digits does not repeat." So according to his definition, 1/3 would be an irrational number, and sqrt(2) would be a transcendental number -- the former false for obvious reasons, the latter because sqrt(2) satisfies the polynomial equation x^2 - 2 = 0. Moreover, this is something that a reasonably bright high schooler might be expected to know -- much less an ostensibly expert math teacher!
   
   In his manifesto "Tracing Proof in Discovering Geometry," Serra attacks two-column proofs, saying that "so many students fail to master two-column proofs that some teachers are skeptical of claims that all students can learn geometry." While I agree that two-column proofs misrepresent mathematics and make proofs unnecessarily complicated, I'll gladly take them over "Discovering Geometry" any day.

4 comments about Painless Geometry (Barron's Painless Series).

1. Since I'm homeschooling my high school sophomore this year, I've been spending time looking at math books. "Painless Geometry" seemed like a good bet. Profusely illustrated (albeit with silly monkey pictures) and written in plain English, it looked like just what we'd want.

   That's until I started actually using the book. First of all, who ever heard of a 300-page reference book with only three pages of index? How are you supposed to find things that way? It's missing things like the base of a triangle (the index has neither "base" nor "triangle:base") and how to label an angle. The information's in the book, but you certainly can't find it using the index. Not only that, but the pages aren't labeled like a normal book, with the name and number of the chapter at the top or bottom of each page. You can't find your place in a book that way!

   There's little depth to the book. There are experiments with pencil and paper, but no real-world examples of where you'd use geometry. Area is calculated in "square units" with no discussion of real units of measure. Pi is introduced with a single paragraph. No explanation is given of its rich history, how it's calculated, or applicability throughout mathematics.

   The oversimplifications in this book may make life difficult later. The book states that all angles are measured in degrees, and the degrees symbol is generally omitted. Whatever happened to radians? In one of the problems, she asks for the area of a circle with diameter of ten. The correct answer is 100 times pi. The book states the answer as 314. That's an approximation, not an answer!

   Then we started finding the mistakes. Typos like "Computer the area of a circle" (page 184) I can live with. It's hard core mistakes like these I can't tolerate:

   The reader is asked to identify what type of triangle has angles of 120, 35, and 35 degrees (page 101). The answer says it's isosceles and obtuse. In reality, it's not a triangle at all, as the angles don't add up to 180 degrees!

   How's this for a statement of the Side-Angle-Side postulate (page 126)? "If two sides and the included angle of one triangle are congruent to two triangles and the included angle of a second triangle, then the triangles are congruent." Huh?

   There's a "super brain tickler" on page 163 which indicates, according to the answers in the book, that for squares, rhombuses, rectangles, and parallelograms, all four sides are parallel! No. Four parallel line segments wouldn't ever meet. Those four shapes have two sets of parallel sides, not one set of four parallel sides!

   .... That tends to leave us with drek like "Painless Geometry."

   All in all, I found this book to be poorly proofread, ridded with errors, badly indexed, oversimplified, and disconnected from the real world. It may be good as an adjunct for a student having trouble with a real geometry book, but only if there's someone around to explain what "Painless Geometry" omits or misstates.




2. On page 16, it is stated that the area of a circle is pi times the diameter. Is there anybody out there who DOESN'T know that the area of a circle is pi times the square of the radius? That error wouldn't such a big deal, except that there are plenty more to come. I don't recommend this book to anyone.



3. I've been meaning to write a review to respond to those on this page for a while. I guess I have used so many math books that contain an error or two that I just can't possibly throw away such a good book over that.
   
   The fact is that we homeschool and my son LOVED this book which we picked up at the library. It is full of wonderful, hands-on work and SIMPLE explanations that make geometry easier to understand than most other books we tried - yes, truly understand because you not only had it explained well, but also "did" something on paper or folding paper to experience it.
   
   He enjoyed it so much that when I picked up another Painless book at the used book store, he wanted to start it that day, rather than waiting 'til next semester.
   
   So I don't know if y'all just glanced at the book or really tried it, but this family tried it and loved it - and I own a red marker so I can cross out the one incorrect answer I found in my edition!



4. Great tool for young mathematicians new to Geometry. Supplements school textbooks -- exercises in the book facilitate review of concepts learned in class.

5 comments about Precalculus (8th Edition).

1. I taught 2 sections of precalculus with this book last spring. This book is well designed for self study. Examples are keyed to specific exercises so the student is directed to use a concept immediately after seeing it employed in a suitable exercise.
   
   My one quibble with the book is the way trigonometry is introduced. It seems to be needlessly convoluted so if you are thinking of adopting it you should read the first two or three sections covering trig. I chose to supplement it with my own notes.
   
   I would recommend this book for anyone who wants to supplement a high school precalculus course with a book that is stronger on theory vs. graphing calculator techniques. There are some very inadequate precalculus texts out there. If you are serious about mathematics and your school is using an approach that employs graphing calculators in a heavy way, you may want to use this book. In that case consider an older (cheaper) edition.
   
   Update: Another reviewer comments that the 7th ed and the 6th ed may be significantly different. Well, they are not.



2. why are the reviews for the 6th and 7th edition of this book the same? is there no difference between editions, such that reviews for the 6th should be kept for the 6th. the 7th edition might have changes that could cause some to review/change a viewpoint about its content. maybe at the core they are the same book/method, but it is overall a different book and the reviews should be kept edition specific.
   
   it is my opinion that amazon will not post this as it obviously not a review, but it my contention that the 8 posted are not reviews of this edition, either. why are they posted?
   



3. At the beginning I was a bit worried about the way the book explains the material. It seemed too simple for a book dealing with more complex subjects in math such as functions, trigonometry and analytic geometry. Then again it could be said that this quality is the one that makes the book such a joy to read.
   
   Not a single time did I felt lost or confused by the presentation. Most of the graphics and photos do supplement the explanation, and help the reader grasp the information better. One of the highlights, one that perhaps most people will miss, is the simple review questions at the beginning of each section. These little snippets of previous material force the reader to review those concepts that will be essential for further understanding.
   
   Every new section in the book is short and clear; thus reducing the amount of explanation, but at the same time maintaining just enough so that the reader will not feel lost in the many formulas and derivations. If this book does not get "5 starts" from my review it is only because it could be more mathematically rigorous by presenting more proofs. But by not doing so it increases the clarity and easy presentation the book possesses - great book well worth the price.



4. Precalculus (8th Edition) is a great textbook. A little on the heavy side (as in the weight of the book, need a wheel barrel to get it around).



5. This is my first time purchasing anything on Amazon.com. I was a bit skeptical and uncertain. I wondered if the book I ordered would arrive and if so, in what condition.
   I was pleasantly surprised when I received the package in the mail. When I opened it, I was alarmed that the book was in such good condition and everything that was mentioned about it was true.
   I purchased a few other books which arrived in the time specified that it would arrive and in the condition that was stated in the ad.
   I have no fear using this site to purchase other materials.

5 comments about Sacred Geometry: Philosophy and Practice (Art and Imagination).

1. Reading Robert Lawlors book took me out of a classroom and into a discussion of the origins of mathematics. Just enough details to all the material covered, making it a breath of fresh air to others stodgy presentations.



2. Great source for a workbook; not an elementary book for the true beginner.



3. If you have been looking for the secrets of the Pythagorian Brotherhood, then look no futher - this is the book. Robert Lawlor takes you step by step into the realm of Hermetic Knowledge and connects it all together.



4. Very, very insightful intro to sacred geometry. If not familiar with this topic, I would suggest one first read the book to get your feet wet in a new way of perceiving what's around you. Then go back, re-read it slowly, and carefully do the math (which isn't difficult, really) and make the geometric constructs on graph paper like the author suggests. You have to do the exercises for it all to fully sink in, and achieve greater comprehension. This book is quietly profound. I only wish it was longer and for this talented author to get into the deeper end of the pool. Lawlor's commentary is often provocative and compelling.



5. Robert Lawlor's book presents itself in a "workbook" type form. It takes you through the process of understanding Sacred Geometry and how to look at, and understand these abstract principles in a very methodical process, by building and developing upon the simplest concept of One. Lawlor has written a classic.
   I have not seen many other books that take this approach as he does.
   He guides the reader to a deeper understanding of how the "unseen" universe works and helps one develop a better perception of that reality.
   The diagrams are easy to follow and the text is well written. It is presented in a simple format that anyone with a true desire to learn this subject will enjoy and understand, this is a great "starter" book and a wonderful reference book as well.