WildTrig0: An Invitation to Geometry: the WildTrig series

[lhyx1990]

i'm a computer science student, and this helps a lot!!! great tutorial!

[jehovajah]

When you do the construction you realise that you have to prove triangles similar and then congruent. It is this second step you fail to do, as Euclid advises .

[jehovajah]

Of course the flaw is in relying on a diagram, and then being careless about the diagram , and the construction. Euclid has no flaws in his advice, which is to construct the figure (or figures!) in question and demonstrate the proposition from these.

Of course, if you want to be duped, believe the "mathmagician"

[Encephalopithicus]

I'm still struggling with your Euclidean "proof" that all triangles are equilateral (I do understand that you are attempting to illustrate a foundational flaw in the Euclidean system, thus the quotes).

Is it not the case that only in an equilateral triangle do the incenter and circumcenter coincide?

If so, it follows that your proof that all triangles are equilateral only applies to pictures of equilateral triangles, not to those of any other kind of triangle.

[vmarciante]

Don't you mean to (wrongly) prove "All triangles are _isosceles_!" not equilateral?

A co-worker and his wife got put off by this right when they started to check out your work. I tried myself to find/make an (additional wrong) AB = AC (and BC) but could not find a way to (pretend) to do that.

[njwildberger]

Hi vmarciante, It doesnt really make much difference. It is more elegant and surprising to ``prove'' that all triangles are equilateral, and once one has ``proven'' that two sides must be equal, it follows BY SYMMETRY

that all three sides are equal, since the argument can then be applied to any two sides.

[vmarciante]

Okay, I follow that. Initially I was not confident/competent enought to find/make that argument. (The fact that all of your other videos explicitely connect _every_ dot made me wounder about a possible mistake in this video.) As you wrote, no big deal, but maybe if you have time (ha!) you could add/edit an "and it follows by symmetry that AC = AB" text bubble over the "AC = BC" part in the video to make it explicite. Please know though, I think that all of your vedeos are wonderful gifts. Thx

[njwildberger]

Hi vmarciante, That is a good suggestion, thanks.

[BeppoProm]

4:43 Why are these two base triangles congruent?

What you really mean is they look congruent, is it?

[salroja]

@BeppoProm no, he means they ARE conguent, the flaw in the proof is rather a matter of logic than optical illusion. Encephalopithecus made the right observation here. (Unless someone corrects me)

[patilnikh]

Sir, when will you write a textbook? I am waiting for it !

[Anonymystik]

I am impressed by your work. I like, when people watches the problems originally.

[Kythos]

I have a question, how do you deal with students with Math Anxiety or Math Phobia? How do you motivate them?

[silencedidgood]

But starting at zero is logical!

[licasamadau1]

excelenta prezentare excelent profesor

toata seria este valabila pentru incepatori

si pentru cei care vor sa-si aduca aminte

[CoauthoredStaircase]

Love your videos- one question- what is it about angle and distance that makes them non algebraic?

also- have people told you that you look a lot like Steve Martin? I keep expecting you to tell a joke or start playing a banjo in the middle of your lectures.

[njwildberger]

Hi CS-- Thanks for the comment. The formulas for angles and distance involve square roots and transcendental functions. People do tell me all the time about my resemblance to Steve M, except he is a lot funnier.

[acmrom]

Given an angle, say 35 deg., how can I 'convert' this to spread? Is it even possible (even though you have discarded the notion of angle)?

[njwildberger]

The relationship between a spread S and an angle theta is: S=(sin(theta))^2.

Thus to find theta given S, take the square root, then arcsine of that. It requires a calculator in general, and is only approximate.

Calculating angles in a geometrical problem almost always dooms you to inaccuracy. With spreads you can maintain complete precision.

[kcenhguor]

Woow, I'm sixty and get very exited about this! Wil follow this closely!

[TyYann]

I just bought your book. Thank you for this very interesting approach.

Keep it up!

Yann

[copetedavid]

awesome video. looking four to go on the journey

ps. love the drum stick as a pointer =]

[loscocolisos]

I have high school knowledge and I found this video extremely interesting! I look forward to the next in the series where Norman will bring Arithmetic, Geometry and Algebra together in order to reformulate the notions of distance & angle! Vivian Ü

[thinkofwhy]

I'm waiting with eager anticipation. But will there be practical examples that clearly demonstrate each concept?