Measure the Earth’s Radius! (with this one complicated trick)
Hannah’s book is out now!
www.waterstones.com/book/ruth...
www.amazon.co.uk/dp/1787632636/
If you have a spare 2⅔ hours you can watch Matt hand craft a protractor. Yes, I know the audio is glitchy. • Matt made a giant prot...
More about Abu Arrayhan Muhammad ibn Ahmad al-Biruni: mathshistory.st-andrews.ac.uk...
This video was made possible by my Patreon supporters for. Those cocktails were officially on you. / standupmaths
CORRECTIONS
- None yet! Let me know if you spot any mistakes.
Editing and filming by Trunkman Productions trunkman.co.uk
Protractors by Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b...
Are you saying that the Shard security did not let you in with weapons of maths instruction?
Please take my upvote and scram
*sigh* very good
I heard this story on a podcast a few days ago. No respect for science by these security people...
Bravo
AHHHHHHHHHHHHHHHHHHHHHHH
"The thing is, we got a number" This is the professionalism we subscribe for.
According to my calculation, the radius of the Earth is purple...
What do you mean the radius is 1.6i+57?
A Parker radius if you will
Plus, they got a positive number... so there you go...
Certainly the professionalism we paid for
Ah yes, the age old joke: “Two mathematicians go to the shard with a fancy protractor and a laser-inclinometer…”
you're taking some liberties with the word 'fancy' there.
Also the keyword there being joke. As this video was the biggest joke I've heard in awhile
that one big prolapser
Thus the origin of the phrase: "up a shard without a protractor."
You were trying to get "weapons of maths instruction" up the shard
“You know what Hannah, it’s a small world” Couldn’t stop laughing xD
I hope you found a chair to parker youself, in case you fell over.
compared to that big prolapser he made
"anything between 10 and a million" the Parker radius, everybody
Findly someone with brains !
AND let's not forget the 100 trillion human second everyone!
A close friend of the Parker Square
Matt: "I've got this really fun idea on how we can do publicity for your book!" Hannah: *sigh* "Can't you just mention it on a video or something?"
*Matt, shouting over the sound of a jigsaw through perspex:* you ever heard of al-Biruni?
Videos of these two together are always so much fun, they’re just a brilliant duo :)
You could do a whole video on the types and accuracy of common units of measure available to the common mathematician with common weapons during the first millennium
I love how Hannah started all serious and embarassed by Matt's antics and got progressively more Parkerish as the video progressed.
Should that not be _Parkeroid?_
So Hannah got Parkerated? No, that sounds so wrong.
By contrast, I loved his realism of being willing to settle for the result not being negative!
@@peterjansen7929 you can tell he's been in a Matt Parker video before.
"Do I have to be with you in the street while you're doing this?" I died laughing! XD
This demonstration is so convincing, I've gone from being a *'Flat Earther'* to a *"Small Earther'*
Isn't that opposite of a flat earther is what Christopher Columbus got wrong wrong when he went to find the western route to the Indies?
@@actua99 Lol the earth is more curved lol
Little steps.
@@micayahritchie7158 isn't that where Columbus went wrong, presuming the earth was more curved and therefore smaller?
@@actua99 idk
"Oi you got a license for that?" "It's a protractor" "Exactly, obviously a weapon"
It was the angle of attack that had Security worried. To remedy that problem, one should use a house brick and a length of string 'x' centimetres in length and attach it to the security guard's testicles.
With very small angles, one could easily cut someone.
They need to see a degree to make sure you're qualified to do basic geometry
"We do not allow tractors here, neither pro nor amateur."
Matt Parker is such a maths geek his body is metric.
I’m glad he’s metric, otherwise his feet would be one foot long.
Everyone's body can be _a_ metric. Most famous one I know of would either be Smoot or the milliHelen
His mind is imaginary though. 🤩
He's built for math.
He's built different
The fact that a Matt cubit is almost exactly half a meter made me actually laugh out loud. That’s awesome.
Reminds me of some field scientists I know of who have gotten like a 10cm or whatever bar tattooed on their arm so they can always have a scale bar for specimen photos
It surprised me. I'm a tall guy and my cubit is about 18 inches (which is fine, as I'm in America). Matt has an unusually long forearm. Very convenient for him, though.
a Parker cubit
this reminds me of the time when we were calculating the speed of muons using two scintilator detectors. But we used rulers to measure the distance between those so we got end result of c+-c. Which is technically correct answer for any question regarding speed asked ever.
The floor here is made out of floor
I don’t get why you got c+-c
@@matthewhubka6350 the speed of muons is really close to the speed of light (something along the line of 98-99%. We had measured it with such a bad precision in distance that our margin of error caused all other values to round up to significant figures so it became (1+-1)c
🤣🤣🤣
🤣🤣
You got a loicense for that giant protractor? -Shard Security
"Pleased to see your maths loicense, Sir."
Do I have to have a loicense for this fleshy pile of meat I control too?
Apply for it at the Ministry of Loicenses.
You beat me to it by 4 hours, my comment: "Oi you got a license for that?" "It's a protractor" "Exactly, obviously a weapon"
Yeah, you think he really knew that fancy word "protractor"?
“Well we’re not going to just calculate the sine of the angle. I built my very own lookup table last night just for that!”
Yes! Nice work! Join the legends people! Derive everything! 😂👍We'll be using a calm sea for the horizon next! You never discover anything new relying on someone else's work... Oh... Well... Okay...so... Of course, you do... But is it ever as much fun?! 😆
I think I still have a copy of Abramowitz tables somewhere...
Disappointed you didn’t find historical look up tables in a library somewhere.
This is the kind of doable experiment that bridges the relevance gap kids experience when learning math(s) in school. It's also a great grounds for relating sensitivity of the outcome to the accuracy of your tools and measurements.
i loved math as a kid and never needed it to apply to anything or have any relevance. and i hated and still hate those who do
@@sharpnova2 why hate people who learn differently to you? That's just petty
@@sharpnova2 stop. do it again and you get the squirt bottle
@@sharpnova2 aren't you the little snowflake lol. I think it would be awesome if this kind of stuff got more kids interested in maths. A bit of fun never hurts.
Another approach is "motor away on your boat until the lighthouse is no longer visible (note however effect goes as sqrt(lighthouse height) + sqrt(your height)). calculate from distance you've gone. No instruments except boat speedometer or your GPS. The square root means your height (which includes waves) can be an important term even for tall lighthouses. Oh yeah, need a pair of binoculars as the light becomes dim. At nine feet the horizon is at 3.5 miles. Seeing the lighthouse just, is its horizon distance plus your horizon from the other side. At 900 feet it's horizon is 10 times further or 35miles.
25:30 I want to say, with the actual value of the heigh, they get a an Earth radius of 708 km. Even smaller
"it's actually professor Fry" Best part.
when?
@@openbordersforisrael 8:28
Professor Fry has a cake.
@@TheBeetrootman Thank you!
As Matt keeps stacking scope-creep onto the required tasks in this project, I can sense Hannah's "I did not sign up for all this" energy.
Yeah, it's like a concerned friend visiting a coke fiend, only to be increasingly put out by the whirlwind they fell into.
@@secularmonk5176 You should have seen the Royal Institution Christmas Lectures given by Hannah, ably (??) assisted by Matt...the whole thing was pretty much that whenever Matt was onscreen!
Matt and Hannah seemed like a great team as they Shard their experiment but then a protractor argument let to them going off at a tangent, which is never a good sine. At least they realised the magnitude of their error.
Matt is the perfect foil for Hannah. I love it every time these two collaborate.
Not for me; fed up with adults acting like a complete tit on TV.
They measured the Parker height of the Shard, the Parker angle to the horizon, the Parker radius and circumference of Earth. Bravo. Well done, Matt and Hannah. And, can we give an Honorable Mention to the Parker cubit? They really did a lot of the footwork in all of this.
Underrated comment! Above par(ker) comment.
Don't forget the Parker Protractor!
The pun alone makes the "Parker Cubit" wonderful.
NOT ONLY THAT but also an order of magnitude does not, as commonly believed, range from n*10 to n*(1/10). Most definitions have it as n*sqrt(10) to n*(1/sqrt(10)), so ~3.16*n to 0.316*n. So when he rounded his 875 up to 1000 it still was not within 1 order of magnitude of the correct answer. You COULD say it was within one... Parker Order of Magnitude 🤡
And they still didn't find Pascal Sauvage before ramadan.
Hannah: This is going to be straightforward, half an hour at the most. Matt: Hold my beer
Hold my protractor
The angle you would have to observe to get the correct radius from 300 meter would have been arccos(6371/6371.3) =0.556 degrees, and to get the radius to be equal to 6322 you would need to observe an angle of 0.558 from 300 meters. So you need a very accurate protractor to get good results.
The Shard is too small. You need a mountain.
Or 0.500 degrees from the actual observation height of 243 metres.
@@g-r-a-e-m-e- That is just one factor. Greater height helps, but you also need more accurate instruments and clear weather to judge the horizon.
I think that the haze on the horizon was the critical factor - without that, the horizon would have been further, so the angle would have been smaller. Lesson learned - use the Burj Khalifa. Higher peak, and (maybe?) less horizon haze.
Its just that those phones are terrible. Also no static stand to stabilise the reading. You could probably get 0.5 with some basic stuff.
Hannah: "We're going to go up the shard with an electrical inclinometer and then do one calculation after looking some stuff up on Wikipedia." Matt holding his makeshift plumb bob inclinometer and cubit shoes: "We are not!"
Matt and Hannah have such great chemistry together on screen. It’s wonderful to see them working together! Especially seeing Hannah get fed up with Matt’s shenanigans.
Agree. They have fun together and it makes 27 minutes go by so quickly. Thoroughly entertaining.
@@raymondsalzwedel I usually watch youtube videos at 1.5x speed especially for long videos but special for this one I watch it 1x to savor every moment of interaction between Matt and Hannah. I literally lol-ing
It felt so good that I felt bad for Matt that his wife would be upset watching this i dont know why 😂
It's an old-fashioned double act. Pretty inane and boring, actually. Very contrived and over-acted with cringing fake and exaggerated reactions. It's just a performance. laurel and Hardy were at least funny.
@@WSCLATER gr8 b8 m8 i rate 8/8
I imagine Matt's "between 10 and 10 million" pessimism compared to Hannah's "within 1000" can be explained by the fact he has estimated pi to a wild variety of decimal places over the years
No, it's because Hannah was planning to look up the height of the observation deck and use a 'fancy pants' inclinometer but Matt was planning on using nothing but his forearm, a piece of perspex and a plum-bob!
Matt's also known for... *ahem* "giving it a go" on a variety of things, and coming out with thoroughly okay results. For entertainment purposes, of course.
@@Salien1999 His calculations for the radius of the earth were NO WHERE NEAR "okay"
@@n-da-bunka2650 if you consider that their angle measurement should have only been accurate to 1° they actually got really close. 0.2 sigma off of the true mean if you calculate the statistical error induced by that angle measurement. Getting your standard deviation down to 1000km takes a stupidly precise angle measurement below 0.05°. I'd say given the tools they had they did amazingly well (ie there was probably some luck involved).
This was once a question in one of our trigonometry tests during high school! We were all so baffled by it, that it became a joke for the class: "I've bought a pound of tomatoes. What is the radius of the earth?"
It's Saturday. What is the radius of the earth?
that's a good bit, now I'm curious how the question was phrased to make it evolve into a joke like that
I'm a sheetmetal mechanic. When I was first learning the trade I worked with on of our companies best mechanics. He could estimate the circumference of a vessel within a few inches by standing a short distance from it (20-30ft or so) and gauging the angle by his outstretched arms. He told me that he learned math while in university in Mexico where he was a top student in the math dept. I think it would be fantastic to have a course all in the "hands on" mathematics. There really are tons of material out there. Some of which is being forgotten.
That's pretty cool
Given that the "correct" angle should be 0.5 degrees, coupled with the stated height of 243 meters to get 6382 km , and 0.4 degrees would result in 9971 km, either protractor would have give a way off result, but it was fun as always, a nice lesson in propagation of error 😃
You need a much taller tower/mountain
And at 0.6 degrees you get 4431 km.
@@augustdahlkvist3998 Well yes, but if you would be on top of the Mont Blanc, it would be 2.2 degrees. So still pretty small angle to measure.
@@augustdahlkvist3998 True, Mount Everest (8849 m) would, if we could see the sea from it, give us an angle of 3.02 (6363 km radius) and 3.12 degree gives us 5961 km.
If you take into account significant digits, the correct angle is 0. For working backwards from the known value, you are taking an approximation accurate to kilometers and adding 0.243 kilometers. Which rounded off properly is still 6391 meters. So the cosine is 1.
"If we round this to a thousand its the same order of magnitude" Can't believe I've never tried this argument on my math teacher, clearly the difference between a pleb like me and a pro.
it's a bad argument, because rounding the earth's radius would make it 10^4, thus not the same order argain.
Eratosthenes did the calculation much earlier, and it was quite accurate. He noted the angles of shadows in two cities on the Summer Solstice.
The process in this vid was also done by a Persian mathematician in the year 1000ad. His measurements and calcs happened to come to a radius within 10 miles of todays value. VERY close, perhaps a little luck involve! His name was al Biruni. You might be interested in googling him
@@37rainman You do know that they said right from the start of the video that this is a replication of the experiment of Abu Arrayhan Muhammad ibn Ahmad *al-Biruni*, and a link about him is in the description of the the Video. No need to google.
indeed. Between Alexandrie and Syene (modern Aswan)
Whenever I want to work out the circumference of the Earth I just pace out the distance from Alexandria to Syene.
Brilliant tongue-in-cheek....😄
Actually Eratosthenes was the head librarian in Alexandria. He just looked up the distance. Important, long lasting civilizations well measure and map their realms. The story about sending someone to pace off 500 miles is apocrypha
"We're off by an order of magnitude" As an astrophysicist, I approve
Pi does in fact equal 1.
I love the way you astrophysicists perform all your calculations to zero significant figures. It shows a relaxed disregard for unimportant little details.
@@xander1052 or 10, whatever...
Or 2. Or 3.... I mean, Hubble's plot shows us a straight line in a cloud, so, nobody can really judge... (Of course, our modern plots are more legitimate looking, but so is most recent science by its own nature)
Well, that's how you get extraordinary precision: Put the difference of 1 and the cosine of a very small angle measured with your phone manually aligned to a brochure into the denominator of your equation.
Instead of using 1/(1- cos x), it would be numerically more stable to multiply numerator and denominator by 1 + cos x, so (1 + cos x)/sin² x. For such small angles (even more so when measured badly), we can use cos x = 1 and (if only Matt had made his giant protractor use radians!) sin x = x.
@@HagenvonEitzen A mathematician in the wild! Fascinating, look how it suggests helpful prose with very little chance of recognition. Truly a marvelous and noble creature.
The lack of uncertainty values and reporting agreement between measured values is *exactly* how you can tell an experiment was done by mathematicians and not scientists lol Loved this
If Hannah was my math teacher I might have actually paid attention in class.
I find it creepy and depressing that they wouldn't let you go to the top with an inclinometer and an attractive, home-made astrolabe.
Could be something about just showing up with it, ask in advance and the chances would be significantly higher ;) At the very least security would know what and why they bring those items, not having to to put their job on the line guessing what it could be used for
The sec guard was not amused by their use of big words.
@hognoxious I don't live in Europe, but I'm still pissed off that the EU made a stupid law forcing every website to make me click "OK" for cookies. Thanks, EU.
The trig battle at 17:34 is the closest we'll get to a real-life wizard duel.
Regardless of the Small World result, you did get an R value and did show the Earth is not flat! Shockingly, a lot of people in the 21st century need to be convinced of that.
Playing fast and lose with "a lot". Don't shockingly conflate noisy activists, with a false idea, being popular in the global town square.
@@quietackshon fair enough. I should have written “too many people” … meaning: “more than zero”. Better?
@@GustavoLovato My comment wasn't really for your, but those that read your comment. Good on you though. 👌
It didn't show the earth isn't flat because the maths is based off the geometry of an assumed spherical Earth
@@Jeoloseph So use their calculations without an assumed spherical earth. What conclusion do you come to?
Going through Teacher's College now here in Canada, and I can't help but be inspired to want to try this with a class of Grade 9 students. Absolutely awesome!
Poor students. What a way to waste everyone's time, while not doing your job of teaching. Are you a teacher or a stand-up comedian/KZhead entertainer?
I am imagining you in front of a classroom full of Matts. Good luck and have fun! :-)
This is why I love Matt Parker. The hard work, dedication, and attention to detail is all there!...unlike the correct answer, but expectations were set. I nominate that this non-negative, _well within_ an order of magnitude radius of the Earth be called a Parker Earth Radius.
parker earth confirmed.
I love Math Parker but holy fork I am IN LOVE with Hannah Fry, and you are too. That laugh. Those brains. Intoxicating.
Chuckled at non-negative.
Also for the record, correcting the height to the observation platform doesn't salvage the result. Changing the angle to 0.5 absolutely does (doing both gets about 6460 km). If your weapons hadn't been confiscated, you probably would have gotten pretty close.
There's also an assumption that there was sufficient visibility that day. Lack of such would bring the effective horizon closer and thus increase the angle.
I don't know why the security doesn't cut off our hands and feet because they are obviously a better weapon.
@@AthAthanasius Yeah, they need a -1° correction. We'll call it the "London Factor".
@@AthAthanasius Not to mention slight elevation changes.
They would have been very close, but largely due to luck. If they'd gone with 0.4° or 0.6° it would have been thousands of kilometers off
This was so much fun to watch. The outcome didn't even matter. I learned something and laughed so much
And it's always nice to see Hannah. ;)
19:46 Hannah: „m please - thank you.“ so british… the units not the politeness. I love that woman
Watching Hannah losing the will to live and appreciating the geekiness simultaneously is a treat it itself
I admire Matt's insistence to replicate al-Biruni's calculation with analog tools. Sometimes it's just so much more satisfying to use the simple tools to craft the answer.
*craft AN answer. It was some way off THE answer!
When you use simple tools, you OWN the answer. When you use complex tools, half the job was done by your tools, and so you've really just glued together a bunch of tools with a teeny-tiny bit of maths.
One of the funniest videos I've seen in quite some time, and it's about math 🙂 I remember in high school, I think we used Pythagoras' formula to calculate the height of a hill using a map for the distance, and the distance from your eye to your thumb. We figured it out my ourselves, and we were super proud 🙂
Absolutely hilarious! And what go my cry-laughing was reading all these comments and reliving the experience again with all the quotes! "The thing is, we got a number!"🤣
This was a blast to watch honestly. Matt's enthusiasm is absolutely contagious.
Matt’s almost child-like enthusiasm (I mean that as a compliment), combined with Hannah’s calm, slightly exasperated, yet kind, patience, make for a great team! (“Yeah yeah yeah, I want to measure the height of the shard!!!”…. (Rolls eyes).. “Ohhh, OK then……..”
_Hannah’s calm, slightly exasperated, yet kind, patience" - well, that sounds like "motherly patience", innit? ;-)
Matt the funny guy and Hannah the straight man A powerhouse of a comedic duo as well as brilliant mathematicians. These two are amazing.
@@toprak3479 It's not remotely funny. It's certainly not comedy. It's totally embarrassing. Mathematicians should stick to mathematics, not trying to act or perform ridiculous skits.
@@PreservationEnthusiast OK
@@PreservationEnthusiast I found it hilarious, not everything needs to be so serious dude
At every single step, Hannah was like "what if we did this part the easy way" and at every single step Matt went "NO! WE DO THIS LIKE ANCIENT GREEKS!"
he was not greek tho, and Matt is trying to teach us how to be dedicated
@@huzefi technically yes, but he studied mostly in ancient greece
@@helloiamenergyman yeah. that kinda makes sense then, i didnt know that tho, thank u
The Ancient Greeks a thousand years ago in modern-day Pakistan? That's only about a millennium and a half too late, and about 2/3 of an Earth-radius away...
@@rmsgrey i think the tools they used in Central Asia were better 😂😂
They should try this again with absolutely old school techniques. Like string to measure the distance between A&B, a mount for the astrolabe, and an actual mountain
I agree. To them, the whole experiment was a joke. The original one was a genuine attempt to measure the earth. Maybe the intent here, was to challenge others to do it better - which should be within the capabilities of most.
You two have such great banter. Very enjoyable!
Hannah: Do I need to be in the street with you? Matt: Yes, I need someone to apologize for me while I count.
At the observation platform, one of you should have stepped, say, 10m back from the window. Then have the other person, still at the window, under your direction, move their finger (on the glass) up or down until it lines up with the horizon. The measure how much lower their finger is compared to your eye height. From that you could calculate the dip angle of the horizon.
Excellent suggestion -- and if I calculated correctly, a dip of about 10cm is a half of a degree (at 10 m). So, they could have possibly achieved about 0.05 degrees of "precision" Now, I need to calculate how far out the actual horizon is and would it typically be visible from that height.
@@fewwiggle From the actual height of the observation deck (243m) it would be about 55.7 km of course this ignores optical effects of viewing from within an atmosphere. While viewing that distance should be easily possible in good conditions that doesn't reflect what we see in the video. There is clear haze present towards the apparent horizon which is a good indication the true horizon may in fact be obscured.
@@seraphina985 yeah, I'm guessing there aren't a whole lot of days in London with 56 km visibility :-)
Fingers crossed the platform is more than 10m diameter, then.
@@tim40gabby25 And, the floor is even :-)
I loved this video! Fun, educational and funny. I love the chemistry between them too. One doesn't need a calculator to figure out how they ended up with an order of magnitude error. For the small H/R and C, we can approximate: R/(R+H) ~ 1-H/R and cosC ~ 1 - C^2/2, so the equation becomes 2*H/R = C^2. 2*H/R ~ 2*0.3/6000 ~ 1/10000. Square root of that: C ~ 0.01 rad or ~0.57° They measured 1.5° - almost 3 times more. That values squared is 9, which gives an order of magnitude error. Detecting the small angle using the mobile phone was the culprit. And the error was magnified by the nonlinear cos function.
Not sure I could convert 0.01 rad to degrees without a calculator. Or Siri.
Hannah and Matt make awesome mathematics communicator's, Matt's can-do attitude and Hannah's down to earth humor is such a beautiful combination 🥰
Did Matt say "Degree to Disdegree" when argue about SIN vs TAN?
That's exactly what I heard too
Yep
Matt Parker has been so active lately! He must really want his million subscriber goal lol
The fact that he doesn’t have a million already is a disgrace to humanity
its october nearing holiday season, KZhead viewership goes up and content creators look for more ad revenue, that is is the reason for more content being pumped out.
I wish I could help more but unfortunately I subscribed a year ago
What was the actual angle that you were trying to measure at the top of the Shard?
just round to 1 significant digit and Matt already has 1x10^6 subs
What a delightful video! Forget the subject matter, that must have been the most entertaining video I've seen for a long time. And I do love Hannah Fry's English accent offsetting - by which I mean complementing! - Matt Parker's Strine (I mean Australian accent).
I admire his dedication to the measurements. A+++
Using the small angle approximation (which is definitely valid here), when θ is expressed in radians, the radius of the earth is given by R = 2H/θ², which shows why having only three times the correct angle causes a change of an order of magnitude.
yup, the angle was definitely less than 1 degree, so being off significantly is going to lead to significant error.
If you two wants to collab each time one has a new book out, I am all in favour of you both writing more books.
A question for Matt; when you were on the street measuring the angle to the Shard viewing platform, were you aiming for the ceiling of the viewing platform, the floor of the platform, or some bit in between approximating your height standing on the viewing platform? All three positions could yield slightly different angles and therefore derive different values for H and also give you different margins of error.
By my math, a difference of 2 meters would have you off by ~10km
@@stephenhenley7452 damn
@@stephenhenley7452 Their biggest source of error, by far, was in the dip-of-horizon measurement from the platform itself. Since they couldn't take their proper instruments up, they had to rely on a very questionable substitute. I'd probably have used a bubble sextant instead.
Honestly, one of Matt's best. Loved this video.
Getting his forearm length surgically altered is serious commitment
"Can you come and look at the angle, Dr. Fry?" "I just need to come around the ... it's actually professor Fry." FLEX ON 'EM HANNAH
Took me a minute, those don't mean the same things in the USA.
Wait, is professor higher than doctor in the UK? Professors in the US are called Doctors
@@jeo1812 A doctor is just someone who has done a PhD. A professor is purely a rank given in a university once you are sufficiently senior in the department. Our teachers in school are just called teachers not professor or anything.
It's such a funny thing... when I was teaching, I never liked to be called "professor." Doctor is a recognition of learning and research, but professor feels like it's just a job title, a recognition of the fact that you did well in an interview or stumbled upon a teaching position with no better applicants. But... I know many people who think the very opposite! (And I suppose the fact that I abandoned teaching suggests that they have a bit of a point?)
@@glenm99 professor is a much more prestigious title than lecturer or associate professor
That was way too much fun! Thank you both!
This is one of the most joyously wholesome videos I've ever seen.
After crunching some numbers, I'm super impressed with Al-Biruni's result! According to Wikipedia, Al-Biruni used a dip angle of 34 arc minutes. This means the mountain that he measured the dip angle from would have been about 312 m above sea level (remarkably close to the height of the Shard if you ignore refraction). By the same logic, you should have measured about 30 arc minutes at the observation deck. Accuracy of measuring the dip has a huge impact on the accuracy of the result. With your measurements, if C is off by a ±0.25° (even with every other measurement being perfect) your error bound goes to about ± the radius of the earth.
It's amazing how we struggled with out modern tools while someone ages ago produced a much more precise result. It has to do with the sensitivity of the angle of course. Essentially, AL-Biruni had an awesome protractor.
@@anil-vc1pd and mountain security was lax on that day.
Very interesting. This makes me think that Al-Biruni's calculation is "too good to be true." Wikipedia also suggests that Al-Biruni did not take into account atmospheric refraction, which by itself can introduce an error of about 20%, so to get within 2% of the true value seems very lucky. I wonder if Al-Biruni knew ahead of time what answer he was supposed to get?
@@JohnDoe-ti2np He just got lucky you think? I can see that happening if the measurement least count is 0.5 degrees but this method can be relatively accurate if you are able to measure seconds.
@@JohnDoe-ti2np Eratosthenes had figured out the circumference of Earth over a thousand years before Al-Buruni, so there is a good chance that he knew this. Eratosthenes calculations were about 5% off.
I've been playing around with the numbers a bit on my end, and you'd actually need to measure to hundredths of a degree from the Shard to get anything close to an accurate result - it seems like 0.52° would get something OK (from your height measurement of 263m which you explained isn't quite accurate anyway), while only a tiiiiny deviation to 0.56° already makes you off by more than a thousand kilometers ; so from that alone, imagine having 200% error with your 1.5° measurement, and it turns out being "only" an order of magnitude off as a result is actually pretty impressive, hahaha! PS: If you wanted to keep only one significant figure, 0.5° would yield 6900km radius, which isn't too bad! :-) EDIT: Also, considering they probably didn't have such precise protractors a thousand years ago, I think this experiment is best done with actual mountains - if the mountain is 2.6km tall, one might assume you could knock a decimal off the protractor measurement to get a similar precision radius measurement? EDIT2: Again not quite apparently - tried the 2630m mountain, 1.65° gets a relatively accurate measurement while 1.6° is roughly 400km off, so I'm guessing they probably had a protractor that was precise to at least a 20th of a degree, which is impressive in its own right :-)
thanks for that. i wondered what the correct angle from the top of the shard was for them to accurately work out earth's radius, for every tenth of a degree out would impact the the radius by hundreds? of kms did you reverse engineer the angle knowing R (6371) and R+H (6371.3) to get around 0.50°
@@ekim613 Oh noooo. I'm a programmer, so I simply did trial and error until I saw values that made sense hahaha! Nothing complicated really :-) just a bit of time on my favorite calculator (Python)
@@cheaterman49 if u were to work it out backwards with those numbers, what angle would you get exactly? no need to approximate an angle when you already have the full equation
@@ekim613 While you're right in principle, I'm not sure it's something I'd really want to spend time doing, I was personally pretty satisfied with an answer that was down to two significant figures hehe :-) but feel free to make your own experiments!
@@cheaterman49 i just did so hehe, quick bit of research and came up with this: A° = cos¯1(adjacent/hypotenuse) cos¯1(6371/6371.3) = 0.5560°
Such great chemistry between you two, it's amazing. Please do more collabs together :-)
So fun episode with Matt and Hannah together. I hope you make more episodes, and that Matt will make a guest appearance at some point on Curious Cases
It's obviously 1 in natural units.
Radius of the Earth, normalized to the radius of the Earth!
As a matter of fact, that's how the meter was originally defined! As 1/40,000,000th of the earth's circumference through Paris. That means the earth's radius is almost exactly 20,000/pi kilometers, off by only 12 kilometers! A nice easy way to quickly calculate the Earth's radius.
Much think Very maths
So Matt and Hannah were right if you round it to the nearest natural unit.
Flameo hotman
You are basically doing 1 minus almost 1. Meaning you're dividing by a number super close to 0. I'd say even arcminutes are significant here.
This was hilarious, and demonstrates the humor in math. Awesome video!
A couple of things. 1. A taller building or something like a mountain would have gotten you closer results. 2 walking further would have gotten you closer results 3 a tripod that you could lock the protractor in place would have gotten you closer results.
I love it when Hannah and Matt make videos together. They have such a unique chemistry and they always nerd out when doing these videos 😁
Can we call 2x Matt’s arm the “Parker Metre?” We can have a whole Parker Unit System with that!
It doesn't fit the brand though, because 1 Parker meter = 1 actual meter, so, I'd have to say with great sadness, it's both redundant and doesn't fit the Parker characteristic.
Either it should be defined as 0.998 metres or it should be used to measure distance down a slightly crooked path as he went round a building and called it 200 Parker Cubits.
@@animarain But would it really be _exactly_ 1 meter? Oh, I think we both know the answer to that.
@@kindlin Well, he's built for maths, though. We definitely cannot deny that!
I'm afraid the parker-kilogram would fall more substantially short, and a parker-second would turn out waaaaaay too long.
The buildup for this gets increasingly amusing, good stuff (as usual).
I hope you continue to plan and prepare as little as possible. I love how you respond to situations like the great protractor confiscation lol.
I am disappointed that Matt didn't build a wheel on a stick and counted the number of revolutions and then multiplied by its circunference to get the total distance. He could've made a bell that would ding at each revolution and count the number of bells without looking at the wheel!
100% agreed.
A wheel, huh? Sounds like a good reinvention.
And a stand or tripod for the protractor.
Well, he really should measure a value for pi first ...
Yeah but it would not have been nearly as funny
"Mathematicians Acting Stupidly for Fun!" Definitely buying Hannah's book, so I can be a real mathematician just like you two.
This was pure comic genius. Loved it!
You can make a much more accurate measurement of the radius without even using degrees, radians or trigonometric functions. When you're on top of the mountain (or Shard) you construct a little triangle with sides a, b and c for yourself as follows: mount two identical rulers upright a horizontal distance b apart such that their bases are at the exact same level. You can match their level to each other by having them together in a bucket of water or using a clear flexible pipe with water (basically establishing a water level to use as calibration). Now line your eye up with the horizon and points on the rulers, thereby measuring the vertical dip over the distance b. Let this dip be called a. Let c then be the hypotenuse. Let h be the height of the mountain (or tower). The radius is then given by R=2*h*b*c/(a*a). The big advantage of this method is that it avoids the sensitivity to errors in measuring angles. Basically, a small error in the angle makes a big difference in the ratio of b to a, but measuring b and a directly solves the problem. Edit The formula above is not mathematically exact, but it is an excellent approximation. For a height of 300m the error is only 0.002%. Even at the impractical height of 400km (ISS altitude!) the error is still only 3%. At low elevations c is for all practical purposes equal to b, so the formula can be simplified to R=2*h*b*b/(a*a). If θ is the angle to the horizon this becomes R=2*h/(tanθ*tanθ). Changing c for b in the formula changes the answer, but interestingly it doesn't change the accuracy - it only changes the sign of the error. So for a height of 300m the original formula gives a radius of 0.002% larger and the "tan" formula gives a radius of 0.002% smaller. This sign change in errors holds for any height, even at altitudes of thousands of kilometres. I share Prof Hannah's love for using tan. You can measure tanθ directly with the rulers and water level trick, obviating the need for measuring θ. Ideally one should do one's measurement where the horizon is the ocean. Doing it on a clear day at the cliffs of Dover would be a good idea. Edit So the exact formula (which holds for any height) is then R=H*b*(b+c)/(a*a)
HOLYY.. I thought of something really similar, but in that case what would be your a? And why b equals c, I was doing some alg and reached to that point.
"Call it 'c'! [...] Yeah, you're looking at it." :D Really appreciated that joke.
They have good chemistry together I always like these two together. And honestly it seems like Matt took every opportunity to do things the long way lol
Seriously. I had a big grin for the full 27 minutes and 30 seconds. Dare I say Hannah is a better comedy partner for Matt than even Helen and Steve?
~ to Hannah's amused annoyance
This is exactly the content I needed right now. Thank you for this amazing video!
Watching you guys together is an absolute riot
These two have SO MUCH FUN together. It's always entertaining to watch them dig into some math quirks.
Of course, The Shard security detail has a "geometry bin". Doesn't everyone?
It's where they put confiscated weapons of maths instruction.
"A large protractor and a laser-guided spirit level? Certainly I'll look. Any identifying or distinguishing marks?"
@@nickfarmer2452 "Okay, we have a 90° and a 180° protractor here, which one is yours?"
For a video about math, this sure has a lot of chemistry
I love all the videos with you and Hannah.
I demand to see a remake with yourself and Dr Fry where you use an actual mountain and the giant protractor.
Professor*
I like to believe somebody within the social circle of that security person will see this video and next time they meet at the pub yell "oi, bruv! you messed up the Parker-Fry experiment, ya daft so-and-so!"
hannah is a total stud, nice work guys this was really a fun video. hope you got more than one cocktail
You both are so funny! I can’t wait to pick up Hannah’s book!
At 22:30 was the moment Prof. Fry realized they had *parkered* it
I have never smiled that much during a math lesson. That was so much fun. We need more of you two interacting on math questions
3:20 Hannah just drew me... Big head, Dunce cap... Nailed it!! 😀
This was really entertaining, you two make a good maths duo