Earthquakes, Circles and Spheres - Numberphile 

A second video is at: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-lubGnk0UZt0.html The new Objectivity video out today is also worth a look: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Sfyd-0tXArc.html

Foolish seismologist: "The earthquake originated from about 30km below the surface." Enlightened pure mathematician: "Or 30km above the surface."

I'm a simple man. I see a Tadashi video, I click on it. Actually, I'm a complicated man. I have thoughts, feelings, and ideas.

MY BOI TADASHI IS BACK

Professor Tadashi should have his own channel, he explains things so well !

I would love to ask Professor Tadashi if he ever considered writing a book about mathematics and physics of our daily lives. I see that he clearly is one of the greatest science communicators of our time (maybe beyond that) and getting to know a little more on his personnal experiences and philosophy towards education, knowledge and such would be a treat. Of course, I hope the partnership with this channel will go on forever! P.S. Congratulations to the animation/edition guys. Superb job making an already didactic explanation even more understandable.

I love his voice. It's very soothing. No morning classes from this guy.

It's funny that the p in p-wave stands for both "primary" and "pressure", while the s in s-wave stands for both "secondary" and "shear". The two polarization components of electromagnetic waves are termed p and s as well. In that case however, p means "parallel" (same in German), while s is German for "senkrecht" (since "perpendicular" also starts with p). Thanks for the great video, btw!

Good job to the animator on this video! Wow!

Zilch is a rigorous mathematical term.

I dare say if your epicenter is above ground you shouldn't calculate but run for the nearest fallout shelter.

Tadashi always amazes me.

I live in northern California, near the Hayward Fault. Before that, I lived closer to the San Andreas Fault. And in my experience living in earthquake zones, the P-wave is more up/down and the S-wave is more side/side. Tadashi's illustration makes sense, but I have a theory that the reason it's reversed in the illustration is because it fails to take depth into account. The closer to the epicenter you are, the more you feel the waves coming from below you, the more vertical the P-wave will be, and the more up/down motion it will cause.

12:51 "What does it have to do with this theorem? Everything has to do with this theorem."

small error in terminology: epicenter refers to the point on the earth's surface directly above the source of the earthquake, itself called the hypocenter. so if a line is constructed between the 2 meeting points of the spheres, the bottom point will be the hypocenter and the point at which the line intersects the surface of the earth will be the epicenter. edit: more trivia: for mid-air explosions, it's the opposite; hypocenter on surface, epicenter is explosion source. the math works out the same except sometimes instead of counting the seconds between the flash and the rumble, you start counting when you go blind and stop counting when your organs rupture. or you don't have time to count.

That idea of measuring the seconds between two waves or between the lightning and the thunder actually has an interesting application in military combat scenarios. Due to the fact that most sniper rifle bullets move at well in excess of the speed of sound, you actually use the elapsed time between the supersonic crack of a bullet going past you and the thump of the rifle that fired it going off in the distance, and you can actually estimate the distance that the enemy sniper fired at you from. If you take that most rounds that might be fired at you from long range have a muzzle velocity of between 700 and 800 m/s (we'll call it at the average of 750 m/s), and the speed of sound is about 343 m/s, and then you account for all the things that slow a bullet down after it leaves the muzzle, like air resistance, wind, gravity, etc., then you get a delay of somewhere just over 300 meters for every second between the crack of the bullet whizzing past you and the thump of the rifle going off. When you hear a crack, start counting (as you take cover, of course). 2 second elapsed means the enemy sniper is approximately just beyond 600 meters from your position. Snipers call the technique "Crack-Thump", and it's extremely useful in helping to find the enemy sniper who's shooting at you so you can engage him and win the fight. Most of you will never need that information, but for what it's worth there's actually a lot of really cool applications for math, mainly for geometry and trigonometry, in long range shooting.

Great as always, but I really enjoyed the low-tec visuals!

'Usually we don't have earth quakes from above', this made my day :) this guy is my new favorite on Numberphile

The epicenter is, by definition, always on the surface (of the earth). The point below the surface, where the earthquake happens, is called hypocenter.

His drawing with him and his baby is absolutely adorable.

I love this video, I studied Surveying in college, and this theorem is right my alley. GPS positioning works on the same basis: you have multiple spheres, each emanating from the one of the GPS satellites, each meeting you GPS receiver's antenna. We can, generally speaking, determine the time it takes for each of them to reach you. With the first sphere, we can place you somewhere in space, on the surface of that sphere. When we add a second sphere, the two intersect to form a circle in space where you might be. Add a third sphere intersecting, and now we have you on either of two points. And just as we don't generally get earthquakes from above, only in exceptionally rare cases are we going to be way out in space. Instead, we can intuit that we are in fact at the one point of the intersection of three spheres... that intersects with a fourth spheroid, namely the earth! Now, since there are lots of variables involved with the measuring the time is takes for each of those radio signals (spheres) to reach you, we can use the redundant data from the spheres of additional GPS satellites to refine our calculated position. So too, 4 or 5 or more seismometers are used to pin point the epicenter of an earthquake!

I would love to have a lecturer who teaches like professor Tadashi. He is excellent at explaining things

Now if i had teachers like Tadashi i might actually have learned something in school lol

Every single school and university should have someone like professor Tadashi

As a geologist this is a wonderful explanation. Love it!

Tadashi-sensei is a great explainer. I could never interpret the difference between pressure waves and shear waves.

I'm a 42 year old man and I just love the playfulness of Tadashi's videos. There can never be too many Tadashi videos so make more :-)

15:30 "-Of course, the epicenter could have been above as well. -Usually, we don't get an earthquake from above" 😂

one of the best numberphile videos of all time

I love the recent increase in Numberphile's animation production value! 💕👌

Lovely animation, it's great to see this channel improving.

Great video and easy to follow. The animations are superb. The tectonic plate spazzing around had me laughing out loud.

The explanations of Tadashi are always so amazing. Great video!

This was the very first time watching one of your videos. I've been subscribed to it for a little while, but never got around to it. Absolutely fascinating.

he draws with words. Its so clear

Both the math and the earthquake calculation were stunning!!

Wow. This is one of my favorite Numberphile videos. I am getting the tingles, because the connections he is able to make and explain so clearly are elegant and insightful

Man, the animation here is so brilliant. I'm always impressed by the animation for the Tadashi videos. Keep up the great work!!

I really enjoyed this video and the creative visualisations too.

I love how professor Tadashi explain things and the animations were awesome

This is what I would call double 'joy of learning' moments

Love the editing and visuals 😍😍 Thank you xoxo

Pretty sure I heard a Wilhelm scream.

Absolutely brilliant, I love prof. Tadahi's videos and great work with the animations.

Visuals of this make me feel like I am back in Beakman's world, basically, I loved them!

Earthquake so strong that it makes Japanese women scream like Wilhelm..

The animations are amazing. Just add perfectly to the great content.

This one has great animations. Well done!

I love his illustrations and animations. I think I say that on every video you put out with him in it.

This was so beautifully executed. His teaching method is so clear, so *graspable*, that I sincerely just want to sit at his feet for a few years and take it all in.

aww, we have baby Tadashi now will this channel still be around when he/she is able to grasp these ideas..

Tadashi is straight-up my favorite Numberphile guest. He always brings something interesting to the table. I wish he was one of the "regulars".

Tadashi is so gifted, they can teach me things I don't understand and, (as is the case today), keep me entertained and interested even when explaining something I already understand.

I know it's been over a year since this was made but this professor is so much fun. He's very clear and easy to understand.

So much love for professor Tadashi but can we also give some love for the person who animated this? I feel like that's like half the video

I couldn't stop laughing at the spasmodic ring of fire

Fantastic! Thank you Professor Tadashi!

Tadashi reminds me of Feynman and some old infamous german orator...He explains things in a way that makes them sooooo obvious and yet 5 minutes later you are astounded that you could think that way.

understood this *completely* this man is a wonderful, wonderful teacher. Tadashi.

Nice. That gives both the epicenter and focus of a quake.

Ah! The animations!

Brady, you have just the coolest job ever.

Really lovely animation, and a very nice explanation for a Californian who should have known this by now.

This circle method of triangulation gives you the distance to the hypocenter (or focus) of the earthquake. The epicenter would be where all three circles intersect.

animations are looking gorgeous on this one

Love the graphics in this one.

Great video and especially great production

Loving the editing in this one.

Beautiful animations and stop motion!

I first learned about this kind of spherical triangulation while playing Eve online. Was really helpful in visualizing the scanning probes functionality.

Fantastic video! Thank you.

Great video, I accept to wait for the next video that shows that we can reject the point from above using 4-dimensional spheres.

Great subject matter, great video. Thanks

Tadashi is the best guest star of Numberphile!

Thanks for an excellent presentation.

The animations are sick..🔥🔥🔥

Love the new visualization style!

The animations in this one were fantastic

Excellent demonstration Professor!

I love Tadashi's explanations

"it's actually a whole sort of circle thing with the ground underneath" Best description of earth ever

Super interesting! I am not sure how exactly I got to this channel but definitely I am subscribing now!

Currently living in Japan, this was quite interesting!😊

The animator behind these videos is also brilliant. Your hard work is much appreciated!

Thank you for sharing this great video!

this is fantastic.. a maths teacher with passion and ability to explain complexity with ease.. considering the copiousness amount dross on RU-vid this is quality.. thanks for posting. am looking forward to more :-)

Beautiful. And very well explained.

ah wow, this is another brilliant one, and despite the simple exposition equisitely intellectually stimulating. well done!

This was beautiful.

12:50 "Everything has to do with this theorem." I loved this line. And it's true beyond "everything" in the example, everything in the Euclidean geometry world, anyway.

Just experienced an earthquake and used his method to check how far the earthquake was, and what do u know, it was spot on 😂

I have learned SO much about earthquakes, thank you!

That was extremely fascinating great video!

Tadashi is my favorite Numberphile

Tadashi's little drawing is adorable!

love the animations!

That was so beautiful and informative!

I love the beginning!

He never disappoints - yet another very interesting mathematical theorem and its application

Excellent educational value. Teach theorem plus practical application in a few minutes .