The Cross Ratio - Numberphile

One of the most famous free kicks ever taken - but how far from the goal was Brazil's Roberto Carlos?
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Discussed by Federico Ardila from San Francisco State University.

The goal was scored by Carlos in a 1-1 drawn between France and Brazil at the Stade de Gerland, Lyon, on 3 June 1997 - it was game one of the "1997 Tournoi de France".

Goal animation by Pete McPartlan

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[Petch]

Never apologize for using SI units. However you are allowed to use any units you like if you can arguing for it.

[nymalous]

I really like this. I especially like the quote he reads at the end, I find it humanizes math (with respect to geometry) somehow. Furthermore, everything in this video is completely testable using simple pictures of landscapes that can be measured after the calculations have been made. I just might try this sometime...

[AbhijayPaul]

This guy definitely has one of the better handwritings of this channel 😌

[eac-oxly]

Man, I have never heard of this cross ratio. What a powerful propriety.

[AshishGupta-qllq]

reading the title i thought it might be about the probability a cross would result in a goal

[gerardmarquinarubio]

people should apologize for using the imperial system, not the metric one

[alexmcgaw]

I counted the stripes on the field. The ball is almost exactly between two stripes. There are 12 stripes between ball and goal line, 7 stripes between ball and centre line. That's 38 stripes in total. The game was played at the Stade de Gerland which has a length of 105m. So each stripe is 105/38=2.76m and hence the ball is 2.76x12=33.16m away from the goal line. Did not expect to get an estimation so close as his!

[redguy]

Do not apologize for using metric system, apologize for not determining error bars.

[judo-rob]

I really like his humility in stating that he learned of it whilst teaching a class.

[evaggeloskotoulas]

this video is a great introduction to photogrammetry

[marksimonelli]

I tried this by taking a photo of graph paper. I ended up with a 5.3% error. I broke up a line into 3 segments. AB = 3", BC = 3", CD=2.25" (known from the grid on the graph paper). Using Photoshop, I found the pixels between these points to be AB=149px, BC =209px and CD=236px. The cross ratio using the pixels was 1.283 and the cross ratio using the know measurements was 1.273. When I tried to calculate the last distance CD using the cross ratio from the pixels calculations, I got 2.37" instead of the know 2.25".Is this lens distortion or correction in digital camera that are throwing off these calculations?

[unknownful]

PROFESSOR FEDERICO!!! I THINK HE'S JUST SO AWESOME!!

[MiguelPereira-ywrg]

Why don't they show the actual goal, just an animation?

[thecakeredux]

Sometimes, surprisingly often, in fact, viewing a numberphile video solves a problem I've had months or years ago in programming and this is one of them. Now I'll go back to years old code and completely change it and make if WAY more optimized, thanks a lot!

[seanehle]

"What we need to figure out is how a change in perspective changes a measurement."
That's exactly what Einstein was trying to do when he developed Relativity.

[PinochleIsALie]

Is it just me or is it cool and refreshing to see real-world measurements incorporated into one of these

[grexursorum]

Nice one! Could be estimated in 5 seconds by counting the stripes in the gras (they are equal distance :-) ) 6 Stripes to the 16, 5m line plus about 6.1-6.2 stripes to the ball :-) Nice Vid. Thanks!

[benhood]

Great video!! Would love to see some more sports-related videos on numberphile. This one was really fun to watch.

[lumpi]

A big "thank you" !. Now I love the cross ratio. Next video : how to shoot like Roberto carlos...

[Sam_on_YouTube]

And now this is in wikipedia. So it is officially an internet fact.