WildTrig0: An Invitation to Geometry: the WildTrig series

Introduces the WildTrig series, inviting you to learn a new approach to geometry and trigonometry. This series will give a careful introduction to rational trigonometry and universal geometry---valid over a general field.

Category:

Science & Technology

Tags:

• WildTrig
• geometry
• trigonometry
• Euclid
• Descartes
• rational
• mathematics
• Wildberger
• teaching
• divine
• proportions
• universal
• quadrance
• spread

[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. 

[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.

[lhyx1990]

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

[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)

[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.

[BeppoProm]

4:43 Why are these two base triangles congruent?

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