> topology-geometry > the-cross-ratio-numberphile

The Cross Ratio - Numberphile

Numberphile - 2018-07-06

One of the most famous free kicks ever taken - but how far from the goal was Brazil's Roberto Carlos?
More links & stuff in full description below ↓↓↓

Discussed by Federico Ardila from San Francisco State University.
More Federico videos: http://bit.ly/Federico_Numberphile

More football/soccer videos by Numberphile: http://bit.ly/Football_Numberphile 

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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Petch85 - 2018-07-06

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

DrZaius3141 - 2018-07-13

In this particular instance, it makes sense to use imperial units considering the 5-meter-box is exactly 6 yards with the 16-meter-box being 18 yards. Then again, rounding those 6 yards to 5.5 meters is much less of an error than you get by drawing with a sharpie on a photo.

TheSuomi - 2018-07-13

Null Null so what's the imperial system based on? Nothing, really, so it's based on the si

Ratib Ali - 2018-07-14

I mean, the penalty box dimensions are defined using yards, so shouldn't that be the default?

Laurelindo - 2018-07-20

I just take whatever crappy units that I am given in a problem and work with those units all the way to the final step, and then I make all the conversions back to SI units, lol.

federico saviano - 2018-12-05

Imperial is retarted

Ashish Gupta - 2018-07-06

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

Deniz Tuncer - 2018-07-06

i had the same thought as well

Antonio Innocente - 2018-07-19

Yeah or the proportion of attacks that lead to a cross instead of going through the centre!! And how the same ratio coincidentally appears in trees or something

Abhijay Paul - 2018-07-06

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

Nym Alous - 2018-07-06

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...

Numberphile - 2018-07-06

Thanks. Glad you liked it.

redguy333 - 2018-07-06

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

Sam - 2018-07-06

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

xooperz - 2018-07-12

+Matt McConaha the outcome would hardly change

Subscribe until Corona virus is over With no reason - 2018-07-12

Sam g

Subscribe until Corona virus is over With no reason - 2018-07-12

Johnny Lee y

Red Baron - 2018-08-10

idk what you mean by this but the Cross-ratio has been on Wikipedia since 2016

redbeam_ - 2019-02-11

@DEUS VULT he means that the wikipedia page for the tournament this goal was scored in now includes the calculated distance

Miguel Pereira - 2018-07-06

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

Marijn Verhaeg - 2018-07-06

Mr. Indelible my guess is that news channels pay to document that footage while numberphile doesn't

Jukka-Pekka Tuominen - 2018-07-07

They do use the footage from the game anyhow. So they'll probably get sued anyway (if that would be the case).

RFC3514 - 2018-07-10

They did use footage from the match, so it's not a rights issue (the goal itself would fall under fair use, as does the footage they used). My guess is they don't want people linking to this video for goal compilations, etc..

It’s Elliot Rowland - 2019-04-01

Article 13. No more needs to be said

David Murray - 2019-08-22

You may find that the goal itself is copyrighted separately from the rest of the footage because it's so iconic.

PinochleIsALie - 2018-07-06

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

PinochleIsALie - 2018-07-06

Jorge C. M. I prefer ending all sentences with semi-colons, since it always leaves people wanting more;

GeneralPet - 2018-07-07

that's a very egotistical thing to say.

Jeremy Shuler - 2018-07-07

PinochleIsALie Found the programmer;

Objects in Motion - 2018-07-11

No its disgusting. Math doesn't need "units".

Jorge C. M. - 2018-08-01

Objects in Motion No, it's*

Siren - 2018-07-06

Belgium won because they watched this.

Venkata Karthik Bandaru - 2018-07-06

Clever way to teach cross ratios.

J.J. Shank - 2018-07-06

Agreed. This approach is brilliant!

Voshchronos - 2019-07-02

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

Sean Ehle - 2018-07-10

"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.

Selarom Ogeid - 2018-07-06

I thought this was gonna be about the ratio between angry people and non-angry people in any given population at any given time.

unknown360ful - 2018-07-06

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

lumpi806 - 2018-07-08

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

Dr. Thomas Rasberry - 2018-07-24

The text from which the stated quote originates is Hartshorne's "Geometry: Euclid and Beyond."

la patria o la tumba - 2018-07-06

I'm just leaving this here:
🇺🇾

gabest4 - 2018-07-06

I just counted the number of stripes cut into the grass. 6+6+little.

X Baron - 2018-07-06

I remember watching the 1994 World Cup that was held in the US and the fields had various crazy grass patterns that were sometimes different in different parts of the same field. The Americans seemed to show off a little there. Another noteworthy aspect was that the fields weren't primarily meant for soccer so they were different size than normally.

Lattamonsteri - 2018-07-06

X Baron that's interesting :D the next world cup is in the middle east if i remember correctly but after that they're in the US again, right? We're gonna see more of those american football stadiums i guess x)

But isn't there a margin for what the football stadium dimensions must be? So the dimensions used in this video aren't absolutely correct maybe?

TheSuomi - 2018-07-13

gabest4 why?

TheSuomi - 2018-07-13

X Baron they have to be standard sized nowadays.

Lattamonsteri - 2018-07-13

Wikipedia still says the length and the width can alter between 90-120 m and 45-90 m so that's a pretty big margin :D But at least the penalty box dimensions and other elements of that sort have a fixed size. Of course they're described in yards and if they're told in metres, they're always like 16.5m or 5.5 or 9.5m. :( Rip SI-units.

Mateus Aquino - 2018-07-06

AGORA O HEXA VEM

Pedro Gonçalves - 2018-07-06

Não parece.

yopassthefuckinsalt - 2018-07-06

Não :D

Fathos Law - 2018-07-06

Quem sabe na próxima.

Marcelo Bulhões - 2018-07-06

Quem sabe em 2022 no quatar

Pedro Possebon - 2018-07-09

tem brazuka em todo lado...

etatauri - 2018-07-07

I am intrigued. I'd love to see more about how this quantity was discovered and if there is some kind of elegant proof I'd watch that as well.

KungFuBlitzKrieg - 2018-07-07

That was damn interesting!

Bruno Machado - 2018-07-07

I actually remember seeing this goal live and thinking "whaaaaaaaaaaaat". The first real wtf moment I can remember

Apricity - 2018-07-09

This is amazing. I just want to say thank you for making these

Jean Bonnefoy - 2018-07-06

Amazing! I already loved math and geometry, now you made me love soccer (well, football, I'm from the other side of the pond)

Felicia Barker - 2018-07-30

I'm so glad you made that 'cross' pun at the end. I was waiting for it the whole time.

Ernesto Marín - 2018-08-27

7:55 yes there is, and i can prove it

Gerard Marquina - 2018-07-06

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

TheSuomi - 2018-07-13

Ferb Freeman we should use base 2 but w.e

Vaithiyanathan B - 2018-10-17

Itachi

Narwhocalypse - 2018-10-29

Imperial units are for those losers who have a flag on the moon!

steelxeno - 2018-11-03

Eh no, the metric system is a bad system to use if you do not have instruments to measure or even use intuitively to estimate a value of distance or volume. The imperial system is a much better system to use when you are trying to estimate distances.

blindleader42 - 2019-04-30

@Kep
I'm going to waste a lot of typing on a complete ignoramus, because of the large number of your fellow ignoramuses that have "contributed" to this thread.

Through all this, you still don't even know that the the United States does not now, nor has it ever, used "The Imperial System" of weights and measures.

The British did not bring the Imperial system with them because said system did not exist at the time. It came into existence about half a century after we divorced the British Empire.

Not long after the French adopted the metric system, the US congress was very receptive to the idea of adopting the metric system, having been one of the earliest nations to decimalize our currency. But the French scientist, who was on his way to America with a gift to the US of a standard Kilogram and a Standard metre, to make his pitch before the Congress, was intercepted by the British and never made it to the US. Remember, in the 1790's the US was still trying to remain on friendly terms with France, while simultaneously staying out of the European squabbles that have been going on for more than a thousand years and continue to this day.

crime ocorre nada acontece feijoada - 2018-07-06

SI>>>>>>>>>Imperial system, aki e brasil

Cecil Henry - 2018-07-06

This was interesting. do more!! I'd like to see how this is derived!!

Roger Beck - 2018-07-07

I really enjoy Brady's productions and I hope he is doing well from them.

J.J. Shank - 2018-07-06

Your handwriting is amazing! :D

Amir Seifert - 2018-07-19

this was amazing and you explained it exceptionally well. thank you. subbed

Evaggelos Kotoulas - 2018-12-11

this video is a great introduction to photogrammetry

Shruggz Da Str8-Faced Clown - 2018-07-06

Now, the real challenge is to measure the arc length of the trajectory of the ball from its kick point to where it landed in the goal box!!!

;^}

Ben Hood - 2018-07-06

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

Numberphile - 2018-07-06

Cheers. Be sure to click on our soccer/football playlist.

dana thurston - 2018-07-06

Beautiful! I have to watch again, I missed one bit...but this is fun.

Matheus Snt - 2018-07-06

GEOMETRY BABYYYY!!!

S T - 2018-07-06

That was beautiful!

Bernardo Fajardo - 2018-07-08

:o I usually love your videos, but although I'm not a soccer fan, my mind was blown with this video!

Shortcut - 2018-07-06

Good luck Brasil, May the best team win.

a Belgian

Albanovaphi7 - 2018-07-06

This is awesome! I gonna try to applicate it in some photos

Kelvin Mac - 2018-07-11

It’s coming homeeeeeeeeeeeeee

WorldOfDeepThought - 2018-07-11

You were teasing us so many times with that goal xD

DoctorSinister1987 - 2018-07-06

That was really awesome. Thanks so much.

safin salih - 2018-07-07

You take the average/median of every newspaper's claimed distance?

Bill Woo - 2018-07-06

v=3ECoR__tJNQ. You really want to watch the replays, not the live shot.

Sam - 2018-07-06

If you count the light/dark green stripes on the field where the ball is placed, you see 6 of them leading up to the end of the 16.5 meter box and then just a little more than 6 from there to where the ball is kicked. This confirms the calculation through an alternate metric.

Henrix98 - 2018-07-06

That's not a link in mobile

Claas Behrens - 2018-07-07

i found this deeply satisfying

Joni Nurmela - 2018-07-16

I thought this had something to do with crossing the ball into the box but ok. Still a great video

Everything Betting - 2019-07-24

I took a load of inspiration from these types of Numberphile videos and made a probability-based football video on how likely you are to win the Super 6 jackpot!

J Bell - 2018-08-13

This is wonderful. I love this.