The perspective image of a square I | Famous Math Problems 18a)

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The perspective image of a square I | Famous Math Problems 18a) | N J Wildberger

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In this episode of Famous Math Problems, we look at the lovely solved problem: how to show that any quadrilateral is the perspective image of a square. This is a question of 3 dimensional projective geometry, but it has a Euclidean aspect because the idea of a square is crucial. In this video we lay some of the groundwork, reviewing basic facts of projective geometry, including the relationships between quadrilaterals (4 planar points) and quadrangles (4 planar lines), more generally the idea of duality between points and lines, and the cross ratio.
This last concept we will introduce in a somewhat novel way, following the approach outlined in the Algebraic Calculus One course, where the cross product of planar vectors plays a key role.
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Пікірлер: 11

@donitarose4225 3 жыл бұрын

There is a genius talking here! Divine gift to fallen humans. Thank you, Dr NJW.

@vincenzocotrone4370 3 жыл бұрын

Very nice and straightforward explanations. Thank you very much.

@DrBwts 5 ай бұрын

Wonderful as always. Although perspective geometry may not be a big deal in mathematics courses nowadays, its is a fundamental subject in computer vision.

@ytpah9823 4 жыл бұрын

That's a very interesting perspective...

@pickeyberry4060 2 жыл бұрын

Video Content 00:00 Introduction 02:17 Projective geometry (quadrilateral + qudrangle) 10:14 Artists perspective of a tiled floor 15:55 Cross ratios and harmonic ranges 24:10 Cross ratio perspective theorem

@gucker 4 жыл бұрын

Thank you for this great video! I am learning projective geometry, and this video has clarified some things for me. I am going to rewatch it carefully again as there is much to learn. Thank you, Dr. Wildberger!

@TupperWallace 4 жыл бұрын

This is great, I finally understand why it works.

@peterhi503 4 жыл бұрын

Brilliant, actually.

@ZachMatics 4 жыл бұрын

Fantastic

@DeclanMBrennan 4 жыл бұрын

I really enjoyed that, thank you. This had the potential to be quite confusing but you have a great way of focusing in on what really matters and making it clear. Maybe I should practice walking before trying to run :-) but at some stage, I would love to see how this is generalized to higher dimensions e.g. the three dimensional "shadow" of a tesseract. Would the Cross Product need to be replaced by Geometric Algebra in this case ?