Divine Proportions 192 192
Divine Proportions  Rational Trigonometry to Universal Geometry  
author  Norman John Wildberger 
pages  300 
publisher  Wild Egg Pty Ltd 
rating  2 
reviewer  David Halprin 
ISBN  
summary  Wilberger presents an ultimately disappointing vision of a new descriptive system for geometry. 
There are various ways to approach Norman's socalled "Rational Trigonometry" and/or "Universal Geometry." I have examined it from various perspectives and it does not live up to Norman's claims, whichever standpoint, that I have taken.
DEFINITIONS
Firstly, the definitions, given in the Introduction:
quadrance = (distance)^{2} = (x_{2} ^{2}  x_{1} ^{2}) + (y_{2} ^{2}  y_{1} ^{2})
spread = (sin(angle))^{2} = sin^{2}A
N.B.When one has an equation to solve, (say it is a quadratic), one expects two solutions and deals with them accordingly. If, however, in order to solve an equation, that has a square root sign within it, then one has to square both sides of the equation at some time and this doubles the number of solutions. These extra solutions are regarded as inadmissible, despite their potential interest and possible geometric interpretation. (See worked example later.)
Here is a point of view which suffices to reject this book on its own merit, whether or not there are any other objections, although many other readers will already know of many other disapprovals to mine.
Let's consider someone proposing new variables in some geometric enterprise. This happened in Plane Geometry (for instance), post Descartes, when some bright sparks came up with Polar Coordinates, Pedal Coordinates, Contrapedal Coordinates, Bipolar Coordinates, Parabolic Coordinates, Elliptic Coordinates, Tangential Polar Coordinates, Cesaro Intrinsic Coordinates, Whewell Intrinsic Coordinates and Euler Intrinsic Coordinates, etc.
There are three essential steps to any such proposal:
 The defining of these coordinates — either in words, with a geometrical description, or in clear mathematical symbology.
 The relationship of these new coordinates with some other planar coordinate system. This amounts to a mathematical statement of a coordinate transformation. (e.g. From Cartesian to Polar and/or Polar to Cartesian.) Once this is so done, then one can transform any previouslyfound equations to the new symbology, and hence arrive at a new taxonomy for plane curves, or a new way of stating the conditions for two lines to be parallel, perpendicular or concurrent, or for points to be collinear or not, etc.
 The demonstration how this new system can be a better system for certain types of problems, perhaps with some limitations in special cases, but not denying their right to be subsumed into mathematical texts, curricula, etc.(e.g. Curvesketching made easier for plane curves, which are expressed in the new coordinate system, if it is to be preferred in selected examples.) Other preexisting coordinate systems have shortcuts to finding such things as asymptotes, cusps, asymptotic circles, poles, points of inflection, maxima and minima etc., so the reader would expect to see similar findings by Wildberger.
This third step, in my humble opinion, is where Norman comes undone, and then some!
viz.1) Wildberger cites many plane curves and their concomitant equations in his new coordinate system, in Appendix A, (pages 279286), but his diagrams have been drawn using software that is dependent on standard polar equations, which are then converted by the software to Cartesian form for plotting. In no way is his "Rational Polar Equation" suitable for being implemented by the software employed. Certainly, any programmer worth his salt could devise a notsoeasy and/or complicated routine to transform Rational Polar Equations back to the regular form, but that is no patontheback for Wildberger, rather it shows the counterintuitive and flawed reason for using that coordinate framework.
viz.2) Wildberger's five laws are merely standard trigonometrical identities disguised by his new symbology, showing no advantage over the original forms. See table in Appendix.
He cites a triangle problem in his first chapter on page 14. He then gives a socalled "Classical Solution" in 5 equation lines, using a trig. table via a calculator, for part of this method.
Then, in the next page, he gives his socalled "Rational Solution", which requires three diagrams and 8 or 9 equation lines, and this is a flawed solution, to which he seems oblivious, and does not own to it therefore.Anyone with a modicum of mathematical sense, who tackles this triangle problem, knows the following:
The usual properties of arithmetic with respect to commutativity, associativity and distributivity also apply equally to common algebra.
When one has an equation to solve (say it is a quadratic), one expects two solutions and deals with them accordingly. However, in order to solve an equation that has a square root sign within it, one has to square both sides of the equation at some time, and this doubles the number of solutions. These extra solutions are regarded as inadmissible, despite their potential interest and possible geometric interpretation.
Viz. The worked example for the rational method for the triangle on page 15 accepts the inadmissible solution as though it is acceptable, whereas the better solution method is the classical method used properly, without recourse to trig tables, and in only four equation lines.
PROBLEM
A triangle ABC has sides a = 5, b = 4 and c = 6.
A st. line from C to AB, (length d), cuts AB at D,
where angle BCD = 45 degrees. What is the length d = CD?
MY SOLUTION
cos B = 3/4 sin B = 7/4, BDC = 180  (45 + B)
sin BDC = sin (45 + B) = sin 45.cos B + cos 45.sin B
sin(45 + B) = (3/4 + 7/4)/2 = (3 + 7)/(42)
d = 5 sin B/sin BDC = 57/4 x (42)/(3 + 7) x (3  7)/(3  7)
= 52(37  7)/2 = 3.313693059
So, in this first instance, Rational Geometry does NOT provide anything worthwhile, contrary to Norman's hype.
In chapter two, Norman introduces a dissertation on Fields, as though this is an important factor for understanding and using Rational Geometry, despite the fact that up to a student's age of 17, schools don't find it necessary to introduce into his/her brain any Field lessons together with geometry and trigonometry.
Don't forget that his advocacy is to replace classical geometry and trigonometry, (especially lines and angles), at school level. He doesn't suggest retaining it and using his methods as a adjunct and/or complement, especially since some of those guys and gals will become architects, surveyors etc. etc.
Were the academic institutions which set college and university curricula, to take Wildberger at his word, by eliminating regular trigonometry and geometry and replacing it with his concepts, it would be the downfall of current mathematical knowledge and standards for years to come. What's more, the damage would take years from which to recover; an almost irreparable predicament in education.
c.f. Cuisenaire of yesteryear.
However, you don't have to read between the lines to see on page 21 that Wildberger excludes 'characteristic two fields.' Although I am not versed in Field Theory, I opine that such an exclusion does not apply to classical geometry and/or trigonometry, otherwise he would have said so. So, he is already implicitly confessing, to a failure of Rational Geometry in the global sense.
I have to confess that I look upon his sojourn into Field Theory as a diversion in the same sense that a prestidigitator (magician), in his field of legerdemain (sleight of hand), distracts the audience members, thereby lessening their attention on what's really going on.
Wildberger then goes into proportions using the a:b = c:d symbology, as though it has more merit than the usual a/b = c/d, like we have in the Sine Rule, say. Warum? Wherefore?
On page 9, he states, without proof, the equation for the spread between two lines. From standard trig, one can easily calculate the angle between two lines, and when one squares the sine of that angle one has his equation without recourse to rational geometry. Now if one subtracts this expression from 1, one obtains the square of the cosine of the angle between these two lines. Naturally if one starts with these two terms and adds them one can see why they sum to unity, which he states on page 27 as Fibonacci's Identity.
A rose by any other name is still a rose, I believe; Pythagarose?
Then Wildberger presents variants of this, all of which are obtained with simple college algebra and are further diversions. Then he waffles on about the possibility of a denominator being zero and its implications. WOW.
(See table in Appendix).
Then, we have linear equations and their solutions using determinants as though it is a revelation. WOW WOW!
At this point, why not reinvent the wheel?
Remember, this book is not aimed at secondary students; such a lower level of presentation is promised in an intended future publication. So, why does he tell us `cognoscenti' so much that, obviously, we would know before picking up his book?
Is he just filling up the pages, due to lack of the Step 3 material, so we are drooling to obtain an implied revelation or other especially informative disclosure?
N.B. We mustn't hold our breath, so as to avoid cyanosis!
So now, on page 31, we have Polynomial Functions and Zeros. Wildberger examines an example in F19, but does not explain why on earth that has any significance in curve sketching. After all, we expect our graph to be plottable in a Cartesian Framework in the usual field of numbers, which we, and our computer plotting software, always use by default.
Page 32 teaches us how to solve quadratic equations by completing the square. This is so deep, that I hope the reader's gray matter can cope, especially since he/she is, presumably, at tertiary level!
Now to chapter 3 starting on page 35: Cartesian Coordinate geometry. On page 40, he makes a special reference to the conditions of perpendicularity of two lines. This is easily calculated since the product of their gradients must be 1. However, he stresses "that this is the single most important definition in all geometry, it colours the entire subject." Then he follows this up by naming this "blue geometry."
So mindboggling WOW WOW WOW! He then promises that other colours will appear. I can hardly wait. I hope the new colours match the colour scheme in my study.
Summarily, there has been nothing from Step 3 to illustrate a finding in Rational Geometry, that gives it an edge, at least. He is just making statements, that are already wellknown in geometry and trigonometry, and he is an associate professor in mathematics, who should be able to do a lot better than that. I opine that he doffed his professorial hat and replaced it with a dunce's hat in order to write such pretentious garbage.
One must address one's audience, or write to one's intended readership, at a consistentlyappropriate level. In matters of a socalled "New Mathematics," he must demonstrate actual advantages, and not attempt to hoodwink us, as he did in the earlier problem on Pg.14 and its badly worked out, socalled "Classical Solution".
If one searches the web, there appears to be no academic interest in "Rational Geometry" by the diasporic mathematical fraternity.
Especially, I had hoped to find that his fellow mathematicians at UNSW would have had something worthwhile to say, and thereby prove me to be an innumerate imbecile for daring to criticise "Divine Proportions."
Alas and alack, niente, gar nichts, zilch. Woe is me. Es tut mit leid.
CONCLUSION
In its present format, a better title would be:
"LE GRAND PURPORTISSIMENT"
This book, overall, is a misrepresentation of the facts. It purports to be what it is not. The promotional literature on the author's web site is descriptive, but more of the author's dream for a mathematical breakthrough than an actual innovation.
If finances were no concern, I would suggest a complete representation of all his original findings under a new title, that states, in effect, that this is a new coordinate framework, that, from time to time, has occasional advantage over the Cartesian Coordinate system, comparable to the other planar frameworks, stated on the first page of this review.
So mote it be. Amen.
APPENDIX

RATIONAL TRIGONOMETRY LAWS 
ANALOGOUS LAWS IN TRIGONOMETRY 
1. 
Triple Quad Formula for collinearity of three points 
Triangular area degenerated to zero. 
2. 
Pythagoras' Theorem for right triangles 
Pythagoras' Theorem 
3. 
Spread Law for any triangle 
Sine Rule 
4. 
Cross law for any triangle 
Cosine Rule 
5. 
Triple Spread Formula for any triangle (Quadrea) 
16 x (Area)^{2} 
Slashdot welcomes readers' book reviews  to see your own review here, read the book review guidelines, then visit the submission page.
Karma whoring (Score:5, Informative)
Why don't you... (Score:2, Funny)
I'm not that Smart! (Score:5, Funny)
Polemic [wikipedia.org]
Tertiary [wikipedia.org]
Concomitant [wiktionary.org]
Re:I'm not that Smart! (Score:5, Funny)
Does the Architect know his thesaurus is missing?
Re:I'm not that Smart! (Score:5, Funny)
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I'm not that funny either... (Score:4, Funny)
A rose by any other name is still a rose, I believe; Pythagarose?
There's also the recurring WOW WOW WOW's which I believe delightfully attempts to break the morose ambiance that prevails throughout the maelstrom of words that the author has deemed fit to call a critique of Wildberger's latest publication.
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Some people just try too hard...
Re:I'm not that Smart! (Score:4, Funny)
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Too bad (Score:5, Interesting)
Sometimes it seems that the only really new ideas being tossed around (outside of lab research and the like) in science are from Wolfram in his book, A New Kind of Science [slashdot.org]. (I do not include creationism in this category because it is not new, so spare me the flames regardless of how you feel about it.) Scientists are great at empirically testing this and that theory but they often have problems altering their own perceptions on existing and accepted information.
I agree with the review that this form of geometry should never supplant the status quo:
Re:Too bad (Score:5, Insightful)
It also isn't science.
Re:Too bad (Score:4, Interesting)
Cellular automatons can "look" like some physical process, but that doesn't mean the two have any casual relationship whatsoever. I think Wolfram forgot that Correlation != Causation.
Or, more likely, he absolutely knows that the work is crap and so he publishes it in a book rather than submitting it to peer review in a respectable mathematical journal.
And, before I get a nasty reply, let me make this clear:
Science is about PROVING or DISPROVING a hypothesis. (Or, at least, making the attempt to do so.) Does Wolfram do this? Absolutely not. The title of his book makes sense, though. It is a new kind of science...the bad/wrong kind with zero consequences or illumination.
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You sound like he ran over your dog :) I find the basic idea of that book is very thought provoking. So what if doesn't prove or disprove a hypothesis? It's really interesting and maybe it could even *lead* to new science in the future. Conv
Re: Too bad (Score:3, Interesting)
"Sometimes it seems that the only really new ideas being tossed around (outside of lab research and the like) in science are from Wolfram in his book, A New Kind of Science."
Really new? No. Tossed around? Oh yes ;)
awesome (Score:2)
A New Kind of Science (was Re:Too bad) (Score:4, Insightful)
Wolfram performs an overanalysis of a very narrow subset of cellular automata while claiming to have invented the field, that 'mainstream science' refuses to look at this incredible discovery, and that his 'new kind of science' based on recursion and cellular automata will change the world, although he has no idea how.
It reads like something written after reading Godel, Escher, Bach, smoking pot, and thinking, "I'm thinking about thinking. Now I'm thinking about thinking about thinking. Now I'm....whoa, I wonder what that looks like on graph paper?"
From the reviewer's notsoclear description, it appears this book falls into a similar category.
geesh (Score:5, Insightful)
"I have to confess that I look upon his sojourn into Field Theory as a diversion in the same sense that a prestidigitator (magician), in his field of legerdemain (sleight of hand), distracts the audience members, thereby lessening their attention on what's really going on."
yes, thanks for providing an explanation for your $10 college words, otherwise we plebs might not have understood you.
Also, what's up with the German and French from out of nowhere? I'm all for using them when there is no easy english equivalent, but what the hell, "Alas and alack, niente, gar nichts, zilch. Woe is me. Es tut mit leid." Those are just extra words.
Re:geesh (Score:5, Funny)
"I have to confess that I look upon his sojourn into Field Theory as a diversion in the same sense that a prestidigitator (magician), in his field of legerdemain (sleight of hand), distracts the audience members, thereby lessening their attention on what's really going on."
"I have to confess that I'm really smart. Smarter than you. In fact, you're pretty damn dumb. So dumb that I have to explain what prestidigitator and legerdemain mean. A prestidigitator does not mean someone who spanks the monkey, and legerdemain does not mean a type of beer. They mean you are dumb."
"Alas and alack, niente, gar nichts, zilch. Woe is me. Es tut mit leid."
"Not only am I very smart, I know more languages than you, proving I am a cultered man of the world. And implying that you are a redneck hick. So suck it, hick, I'm going to go prestidigitate my legerdemain."
Hope that helps get you started. If you want to learn more Pretentious Geek, please first stick a broomstick up your ass and tilt your nose upwards at a 45 degree angle, it helps the learning process.
Re:geesh (Score:4, Informative)
also, it's 'es tut mir leid, but I'm not picky.
Re:geesh (Score:4, Insightful)
Pretentious, yes, but not Geek. Geeks strive for welldefined, unambiguous terms, rational organization of subject matter, and language that accomplishes exactly as much as is necessary, and no more. Geek writing is efficient.
The OP's analysis is excellent, but frought with writing that goes beyond pretentious. It's just bad. Disorganized, rambling, semicoherent and full of useless jumbles of letters that communicate nothing.
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So... somewhat above average for Slashdot then?
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Easy to explain: Legerdemain (sleight of hand).
It amplifies the prestidigitator (magician) author's drama induced authority.
Re:geesh (Score:5, Insightful)
Frankly they both bored the shit out of me after about 5 seconds. Why is it that math is always rendered this way? I've met interesting and articulate mathematicians before, so I know they exist...Are they not allowed to write textbooks? Or at least write reviews about textbooks?
I was pushed into a nearhatred of math by hordes of pretentious math prodigys that had zero use for any student who didn't start off with what they felt was obvious knowledge. The text book talks down to you, the professor talks down to you, and god forbid you ask for a practical example!
I'm not a math genius, but I'm damn good at practical math. The only way I managed to pass calculus the first time was because I happened to be taking it at the same time as a physics course, and I could figure it out where I could see an application in physics. For calc II I shopped around, trying to find a decent book with dismal results. Ended up dropping the class, and shopping for a decent professor the next semester.
Math is cool, but goddamn, the way it's taught is awful and jackasses like this reviewer and the joker who wrote the book he's reviewing are a prime reason why.
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The symptoms you describe exist in every field, from math to literary critisism to welding to surfing.
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Math is just as bad, and the thing is (unlike literary criticism), it shouldn't be! If you're doing theoretical math, you shouldn't need to be walking around trying to convince people what a big brain you have...you're doing theoretical math. Now if you're doing lit crit, you gotta t
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"Nothing like one mathematician being snarky about another mathematician."
Only one of the protagonists here appears to be a mathematician.
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"Physics is to math what sex is to masturbation." (Feynman)
Re:geesh (Score:4, Insightful)
As to your prior experiences, articles like these are part of the reason why mathematicians are distrustful of people that don't find a way to prove themselves. It's an easy field to claim that you've come up with a result, and sometimes it can be a very technical logical fallacy that defeats your efforts. I just wasted a half hour of my time looking up this guy's name for any signs of credibility and reading through the comments.
In experimental fields, even if someone isn't very good, at least they can be used as a technician or research goon. In math, if you're not bright enough to come up with results, you're a nonstarter. I know an undergrad who spent four years struggling through basic undergrad classes with the goal of grad school, and then got to his senior year and none of them would take him. It would almost have been a service if someone had been more blunt earlier on.
Of course, I'm not really talking about the calculus sequence, linear algebra I, that kind of thing. Those are more for engineers and scientists. But there you have to bear in mind that to math majors it's the equivalent of Humanities_Course 101, and I dunno about you, but I've taken my share of shittyass 101 courses. It's usually because it's foisted off on the newest professor that can't get out of it, they in turn foist off a lot of the work on the TAs, and it's not interesting for anyone's research. It's not a great situation, but then again there are exceptions. I went to a small, teachingfocused school, and my math professors were very personable and great teachers. They loved student research because they got so few who were motivated. I spent some time at a research school, and had a lot more opportunities, but the professors were a lot less accessible and not as good at teaching. It's a tradeoff and something worth thinking about before you settle on a school.
Maths As A Science (Score:3, Insightful)
Because there are two types of mathematics practiced in the world today. Mathematics that follows the scientific method, and mathematics that does not follow the scientific method. The latter is regarded as a more laudable endevour.
Mathematics that follows the scientific method is the kind most geeks are familiar with, and which most engineers and ph
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.
If you want to see how a REAL scientist writes, without sound pretentious, but yet writing clearly without unnecessary obfuscation, check out anything by Richard Feynmann for
Some interesting comments about... (Score:5, Informative)
My idiosyncratic take (Score:5, Insightful)
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Except of course, the reviewer's prose is so baroque it is impossible to tell whether is arguments are actually inconsistent.
Re:My idiosyncratic take (Score:4, Interesting)
.
But the irony is that despite the author's pretence, the review is horribly written and not clear at all. I'm a physics grad student, I've read my share of poorlywritten texts and articles, but in even those instancs, at least, does the author convey his message in some understandable way.
.
This review was atrocious, yet the author prides himself on his ability to use a thesaurus. It seems he wants so badly to be admired as a Renaissance man, yet he only comes out looking foolish.
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Dunno if it's fixed, there used to be a bug in slashdot that the first paragraph separator didn;'t work (not sure if it's been fixed). so i inserted a period so it didn't matter. i added a sentence and forgot to take the first dot out.
btw, there should be a paragraph separator here, between the italicized quotes and my reply, if not then the bug is still there.
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WTF? (Score:2)
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SINUSOIDAL FUNCTIONS on a CARTESIAN PLANE?
(No, wait, that was ROBERT Mc ELWAINE! :)
El Sucko (Score:5, Insightful)
I have an M.A. in Mathematics. I've read some of the "Rational Trigonometry" online before, and yes, it is pretty oddball and has its weakness and can be criticized.
But this review is borederline psychotic. It is poorly written, full of ad hominem attacks, lots of madeup grammar and word usage, wierd random abbreviations... it's scatterbrained, repetitive, and unnecessarily hostile.
There is a critical review to be written about "Rational Trigonometry", but this isn't it. I may not like our current government, but I'm still not going to listen to some incoherent homeless guy raving about it on the street.
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And you don't have to, there are plenty of them on
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Not to mention imprecise. In two instances the reviewer says
in order to solve an equation that has a square root sign within it, one has to square both sides of the equation at some time, and this doubles the number of solutions.
which is not true in all cases. Two examples are
\sqrt(x) = x, which has two solutions before and after
New obligatory quote... (Score:5, Funny)
*blink*
"Ya hurt yer what?"
Sack the reviewer (Score:2)
The review, for its content, is perhaps as useless as the book he'
Philosophically/Ideologically driven blather (Score:5, Interesting)
Wilderberger's stance  that there is simply a finite "biggest number" and we shouldn't use or allow anything "bigger", and the resulting implications for irrational numbers  is just baffling. I'm guessing it is the extreme (and from what I can tell surprisingly uninformed) finitist philosophy that drives his Rational Geometry (he needs to somehow eliminate noncommensurable/irrational quantities from geometry lest they interfere with his fear of the infinite)  to him the superiority of Rational Geometry is presumably clear, in that it aligns with his extremist philosophy. The problem is that his philosophy seems, at best, half baked. He seems like a mathematician who took an interest in philosophy but couldn't be bothered seriously reading or considering any of the vast amounts of material on philosophy of mathematics. That is to say, he is, in many ways, little better than this lunatic ("Cubehead") [graveyardofthegods.com] who is hell bent of redefining mathematics to fit with the pronouncements of his idol, Gene Ray (creator of Time Cube), regardless of how shaky the grounding philosophy may be.
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It's Friday (Score:5, Funny)
A very odd mathematician (Score:3, Informative)
(For the uninformed, consult Wikipedia [wikipedia.org]. For a very precise breakdown of these axioms translated to primitve symbols  Wikipedia still includes some higherlevel defined symbols that Wildberger objects to because he can't seem to understand them  see the metamath version [metamath.org]. In other words, there is nothing fuzzy or ambiguous about these axioms.)
His set theory rant created quite a furor on Usenet, here [google.com] and here [google.com].
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This number may grow with time and might not even be bounded, but at any given time, numbers larger than this number (and almost certainly most of those smaller) are physically meaningless. So go on playing with your infinite and t
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I try to keep abreast of the current absolutely correct, final theories of everything.
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The question of whether 0 is a physically legitimate number hadn't occured to me. As a denominator it surely isn't legitimate, and may be illegitimate as a factor in some situations. Quantum effects in the vacuum seem to preclude zero energy.
Newton's laws and the curvature of space seem to have no bearing
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cranky indeed... (Score:2)
This guy sounds as if he needs to do an introductory course in discrete mathematics.
And he gets published????
What a crazy fsck'd up world
I assume you meant... (Score:2)
Compensating for something? (Score:4, Informative)
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There are a lot of math crackpots out there... (Score:4, Interesting)
Didn't bother to read it (Score:5, Funny)
#1  Humble my ass
#2  Such excessive sesquipedalianism is an immediate flag that the writer is writing not to inform or help. He's just masturbating his brain in public.
#3  Humble my ass
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Let's not force everyone into monosyllabic commentary by attacking erudite prose.
strike
OK, stepping way out on a limb here... (Score:3, Insightful)
A few upfront things:
IANAMathematician;
I appreciate the reviewer's efforts to thoroughly discuss the reviewer's point of view;
I don't mind acknowledging that I'm not as smart as the vast population of Slashdot, but I like math even though I'm not topnotch;
I love to learn stuff, and like to read Slashdot articles/comments that are out of my field, and way over my head;
With the above said...
I don't mind looking up unfamiliar terms that appear in an article or in a review (I like learning)  when the words are concerned with the subject matter at hand. I do mind when I read something that attempts to completely fill up my "new word of the day" calendar (for the next millennium). Why? Because I'm interested in understanding the subject and the review, not in how many new nontopicrelated words and phrases that can be crammed into a paragraph.
Lastly, a good review, IMVHO, is one that does not chastise, scold, or belittle the matter of review.
How about a more qualified reviewer? (Score:4, Insightful)
Wildberger may be a little "out there" (alright, he's completely nuts), but this point is not one you can fault him for. There are a LOT of results which exclude fields of characteristic two. It's not a big deal. In fact, it's commendable that Wildberger has explored the ramifications of his framework in any fields with nonzero characteristic, as the "normal" pedestrian conceptualizations of geometry don't apply.
It would have been nice if /. could have posted a review by somebody who is actually qualified to critique the book. And no, I am not such a person, but I know a couple people who are.
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It is an interesting idea which simplifies the calculations in some cases by working only with intermediate values that might otherwise have to be square rooted and resquared otherwise. However, it is not easier than trig in any re
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Review is an obvious troll (Score:2, Informative)
The obvious mistake in the distance formula and the interpretation of the "fields of characteristic 2" exception are intended to rile up people who *are* familiar with these things.
Very nice link... (Score:2)
Grrrr...
"Mighty oddsounding?" (Score:4, Informative)
"what's really going on" (Score:2)
Like using big words to disguise a blatant troll, perhaps?
Jessica Alba (Score:2)
distancesquared? (Score:2)
This is a definition of distancesquared with which I was previously unfamiliar.
But it works! (Score:2)
Proposal to Slashdot Editors (Score:2)
Fields (warning, this post contains math) (Score:2)
Was that meant to be English? (Score:2)
Well, since you welcome comments... (Score:2)
Seriously hope you don't write for a living... and if you do, kindly let me know where that is so I can avoid it like the plague!
I mean, WTF?!? Are you choking on a hairball or s
Ramblings of a madman. (Score:3, Insightful)
Sigh... I'm irritated by people who think that their large vocabularies make them good communicators.
Does reviewer remember high school math? (Score:2)
Still, I can't believe the reviewer took 4 lines to find the length of 'd' in his example. He points out how the author used 7 or 8 lines to do it. That's what makes this ironic to me.
Has the reviewer ever heard of two delightful little formulas known as the Law of Cosines and the Law of Sines? I got the same answer in just two lines, personally. Perhaps no
Gotta ask the reviewer .... (Score:2, Interesting)
Didn't get a good grade, but the resulting stunned silence from the class was worth it.
Reviewer has wrong definition of Spread! (Score:2)
[In Wildberger's line notation, a line L = < a , b , c > satisfies the equation a*x + b*y + c = 0 for all {x,y} in F^2]
The reviewer is entitled to his opinion, but does not have the right to present false information as fact. Definitions are very important in mathemati
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Wikipedia is down ATM with no explanation other than technical difficulties. All subdomains are affected, too.
Ten minutes have passed since you posted that, and I am seeing Wikipedia just fine.
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I experienced problems with wikipedia today as well, so I guess it was just bad timing posting it just before wikipedia was up again...
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It was down before I left my workplace today and wasn't up when I logged in at home again, more than two hours later. It's back up right now, write access is slow but possible. Let's see what Wikinews is saying about that...
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Re:mod parent troll (Score:4, Funny)
Those who spend their day monitoring the status of wiki shall receive no slack.
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A BulwerLytton candidate [bulwerlytton.com] to be proud of!
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You are incorrect. Take an equilateral triangle each of whose sides is 4. Then the altitudes are 2*sqrt(3). Let ABC be a triangle, and let AD be the altitude from A to BC. The AD is no longer than either AB or AC.