This may be true ... but have you tested this with a Van de Graff generator? 😁 Isn't there a large generator in the lecture theatre where they hold 8.02?
I think u should try to focus on ur future like being a scientist or something else instead of doing videos on internet n wasting ur time follow a chemistry ideal women Marie curie who gave her 12 year life to research only on radiation n due to radiation died for our better future
Or the one where, if out of 100 possible questions there are five you cannot answer, those five are the only questions on the exam ... even though you only have to answer any four out of the five.
One day (in university) I studied my whole week for a finance test on the day of the exam it was the human ressources teacher that showed up, my finance test was the next week ...
I thought my college biology exam was on Wednesday, but it was on Monday. I learned this when the teacher told us to put away our notes and binders. I somehow got a B on it, despite never studying.
4-6. No kidding. Astonish me. I can't wight. Or is that a weight of an unstable element. 4-6. Hmm . Are you changing me? Let's go smarty pants. U were saying??????
More than 2 though, they were all also infamously involved with the occult, and they were all interested in separating a technocratic master class from the rest of humanity... that is not these 2 girls but definitely Einstein, Newton, even Ben Franklin, Pythagoras, really anyone who was ever a key figure in this field
fustrum is a part (rather: portion) of a 3D solid between two parallel planes cutting it (or passing through it). it's what remains when some really bad person cuts away both ends of a bread loaf. :oP
To me it sounded like a German word but apparently it's derived from Latin for "crumb", so you know I think you're bloody onto something with your bread theory.
@@Dractonis I assure you, 'frustum' is not even close to a German word. The German version would be 'Kegelstumpf' or 'Pyramidenstumpf' depending on what geometric body you based it on.
Wow😃😃😃 never thought you will Collab with each other. You both are my favourite TH-camrs and I am so happy to see you both in a single frame. Please do more such Collab in future also
Great Video!! it was good seeing a older tests from one of my favorite technical and mathematical schools. Its interesting how simplistic mathematics was back then and how difficult and well fleshed out it has become.
My first thought was that the problems are hard for us because we don’t know the foundation of an 1876 candidate and what he was allowed to assume. Then I realized that - yes, of course we know! Given the year, I suspect that these are all propositions from Euclid’s “Elements” (or at least some are) and the examiner want to see you reproduce the exact argument used by Euclid.
2:55 I've paused the video. *1)* True. *2)* True. *3)* True. *4)* By the Interior Angle Sum Theorem & dividing by 6, each interior angle of a regular hexagon is 120 degrees. An inscribed regular hexagon will have each of its interior angles bisected by a radius of the circle, producing angles of 60 degrees each. One side of the hexagon and the two radii intersecting it form a triangle. By the Interior Angle Sum Theorem & subtracting the 60s on the hexagon side, the angle formed by the two radii measures 60 degrees as well, thus the triangle is equiangular, which is then equilateral. Therefore, the radius is congruent to the hexagon side. QED. *5)a)* Definitions: The frustum of a pyramid is the portion left after chopping off the apex with a plane parallel to the base. Lateral area is the combined area of the lateral faces of a prism/pyramid/frustrum/cylinder/cone; in other words, it's the surface area minus the base area(s). *5)b)* Proof: The lateral faces of a pyramidal frustum are trapezoids, each with the same height, which is the slant height of the frustum. The lateral area would be the sum of all of the trapezoidal areas of each face. By the distributive property, the half-height of the trapezoid area formula can be factored out from that sum. By the associative & commutative properties of addition, the remaining addends can be rearranged so that all of the "upper" base lengths are together and all of the "lower" base lengths are together. The sum of the "upper" base lengths" is the perimeter of the "upper" base of the pyramid, and the sum of the "lower" base lengths is the perimeter of the "lower" base of the pyramid. Therefore, the remaining expression is one-half the slant height of the frustrum multiplied by the sum of the perimeters of the bases. QED. *6)* The instructions state to skip problem 6, which is good because I have never heard of a "polar triangle" in any non-geography context. Based on the wording of the prompt, though, I would imagine it has something to do with reflection. *7)a)* Cone: Volume = 20pi u^3, Lateral Area = 65pi u^2, Total Surface Area = 90pi u^2 *7)b)* Cylinder: Volume = 96pi u^3, Lateral Area = 48pi u^2, Total Surface Area = 80pi u^2 I've given 9th-graders who were bad at math harder geometry tests than this, & they almost all passed.
_Vocabulary on the test:_ Chord = A segment connecting two points on a circle. Secant = A line which intersects a circle twice. (Contrast a tangent, which only intersects a circle once, & yes, the trig functions are named after these lines.) All secants contain chords. Subtend = Painfully awkward term for "to separate a circle into arcs with a chord". Intercepted arcs = Awkward but much more common term for "arcs bounded by these lines". _Vocabulary in my answers:_ Apex = The vertex of a cone, or the vertex of a pyramid where all the lateral faces meet. Addends = Things that get added together. (Compare "factors" in multiplication.) QED = Quod erat demonstrandum, Latin for "that which was to be proven". Indicates that the claim has been reached logically so we're done with the proof now.
it is badly phrased by modern standards. the command term "if" defines/supposes a statement, and therefore without a further command isn't really a question. It should have a prove or disprove in there somewhere
I went to school in the 70's and the words arc, chord, subtend are very familiar words. I'm not sure if I know any words that can substitute them. A 'regular' pyramid is a pyramid that has all the sides of the base equal and the slant height of each face is equal.
It doesn't matter as much to forcibly remember the shape "frustum" as it does to have the insight into solving the actual problem. This has been a learning moment. Thank you!
Honestly I was wanting a collab b/w you and Diana a few days ago and this came to me as a surprise... Beautiful video! And the questions without any "question" was a new one... 👍🏻
A fustrum is a conic section and even the phone intelligence questions the word,, ignorant phone,, . A fez hat from Morrocco would be the fustrum shape. I think we say fez . With regards to questions about where's the question , well those slack days are today back with us with a number of errors occurred in the year 12 physics exam for HSC in Victoria Australia in just last few weeks .
A secant is a line drawn through a circle thats not right through the centre. A trig secant is the reciprocal of the cosine ratio of triangle sides. Why are our primary used trig ratios sine (o/h), cosine (a/h), and tangent(o/a) and NOT sine, secant (h/a), and tangent is lost to history. (FYI: cosecant = h/a, cotangent = a/o, covering all 6 permutations)
Those questions are NOT talking about the centriod of the object BUT the bisects of each side. ( I also thinking, to bisects the base as it is one side of the shape and another side to find target frustum shape )
I know, late to the party, but I have a question. Could it be that question #1 was the instruction for how to cut the sides (4x) of the pyramid to create the frustum? Maybe they wanted the top perimeter to be one-half the length of the bottom perimeter. I think.
Slightly different way of thinking about question 5: Rather than computing the area of each trapezoidal lateral face, one can combine the faces to make a single parallelogram, and calculate that area. This way of intuiting imposes an extra step in the proof, but it's how I arrived at it ^^ Thought that was slightly interesting.
So, for the 1st question. You would label A as the left edge, B as the right edge D as the small bottom edge and D as the big bottom edge. We know that if triangles are similar then the ratio of their edges are equal: ((1/2)A)/A = D/C => 1/2 = D/C => D = (1/2)C. You can totally use numbers and variables! I wouldn't consider a verbal proof to be sufficient lol. Not trying to diss you, I definitely enjoy your content and respect you :)
It's crazy that I was taught about the frustum of a pyramid in 9th grade in Nigeria. I'd always assumed it was a commonly known word among scientists lmao
Great to see historic test. Would be great if you could get a historic exam from Cambridge Uni and see what Newton's exams were like. Or the oldest exams you can find... Also my mom wasnt 'allowed' to study physics in a very elite highschool in 1950s because she was female. I assume MIT didnt have such issues in 1800s?
The first one is so easy , that use the intercept theorem . If you have a triangle ABC cut by this parallel line in points D and E then AD/AB=AE/AC=DE/BC and so ((1/2)AB/AB)=DE/BC so BC=2DE
If you add "Specify the resulting geometric shapes and their properties (if)..." to the first two questions, you get a reasonably complex and sensible test of the student's understanding of mid-level Euclidian geometric concepts.
Feels to me like this is an oncomplete sheet. Like the sentences in the objectives relate to like a picture of an object or situation explained on a seperate paper
- I had so much fun (and confusion) with this video. - I get the impression the first three statements were asking if they were "True" or "False", required the use of a drawing compass, and the student was being asked to scribe (show) their work. - Note: #1 doesn't specify the type of triangle and it would be "False" for the scalene while "True" for the isosceles and equilateral. - Notice how most of these questions could have a nautical navigation/cartographic application? I wonder how many applicants knew how to use a sextant?
Hey! I am not sure if I got it wrong but in the final problem, the first part, the lateral surface, 'h' was assumed to be Height and NOT Slant height, but in the second part, to prove its half the sum of both the perimeters multiplied by 'slant' height, it is still multiplied by the same value 'h'. Please feel free to let me know if I missed something. Was fun to see you folks do something interesting like attempting a centuries old exam paper. Cheers!
As as retired master mariner before the days of GPS, nay, calculators. We used astronomical almanacs, sextants and tables (Norie's and Burton's in the British commonwealth). Various functions of angles were tabulated to simplify calculations. The secant of x is 1 divided by the cosine of x. We also had the haversine of x which is 1/2 of 1 minus cosine x. Also, I think that the polar triangle, in the question, refers to triangles drawn on a sphere. Spherical trigonometry, the basis of navigation. It was long time ago and I might have dreamt it all.
for #1 -#3 i believe they only expect a labeled diagram. your #5 def needs to mention the upper base is parallel to the lower. the prime notation for #6 means the A'B'C' is a transformation of ABC. just guessing, my math degree is from the '80's, before graphics calculators, and barely personal computers using floppy disks.
In the first problem, I think the answer could be that the triangle is an isosceles triangle. Or, perhaps this is a true/false question. I think the next two are true/false questions as well.
This shows the importance of knowing what words exactly mean. Once you have the definition of "frustum" the frustration stops and the question becomes accessible. I wish teachers and schools would pay more attention to definitions and dictionaries, also outside of MINT subjects. A textbook that uses terms before defining them is unnecessarily confusing.
frustums are used a lot in computer graphics as the plane of the camera (screen= top of pyramid) and then how far that camera sees (far plane = base of pyramid) and removing parts of object not within the frustum that cannot be seen. Wonder what they used them for in 1876!
I learned what a frustum was at school, but I next encountered the word while reading about the space shuttle's solid rocket boosters, where the frustum is the top of the booster where the parachutes are stored.
The nosecones of the space shuttle solid rocket boosters are called frustums. They've been in plain slight for decades! 🚀 "Everyday Objects for $1000, Alex."
Hi @tibees I just love U're videos and the reason for it tat u Makin videos on different subjects (like physics , jee etc) which is quite unike and great keep up the good work. 👍
Hi @Tibees, just a suggestion: use a mic filter or a sock to remove the sharp spikes in the audio. Your voice is really relaxing in most of your videos but the spikes really lowers the quality. Other than that, cute nerdy content that I will definitely want to watch more of. Thanks! :)
@@jitadipmukherjee3127 frankly I think on an average all the Indian entrance exam for institutes and civil services are way tougher than their foreign counterparts
Duh it is. This is from 143 years ago. Very few people knew any sort of higher level formal math at that time. Knowledge is built on over time which ends up as us being taught this level geometry when we are ≤15.
I think you were most of the way there on #1, Toby. I think they wanted you to make two more triangles on the bottom so that their two bases are each congruent to the base on the top triangle.
This style of just giving a statement and expecting you to prove it is common in mathematics textbooks. A polar triangle comes from spherical geometry.
Line numbered one hints at the ability to take a triangle and bisect it in a way where you can then calculate the area of each portion towards then getting the sum of its total area. 😉 [ th-cam.com/video/lag22Hl2RQw/w-d-xo.html ]
Exam shown from 2:51.
Would you be able to pass it?
Will definitely try.
I am a Mechanical Engineer & a Physics and mathematics enthusiast. I will surely attempt.
Immediately came here after watching physics girl
No
Pass I very seriously doubt; are there still marks for an incorrect attempt? The 1st three questions there was I thought a correalation of 1 example!
Key point learned from this collab: long blonde hair game is strong for physicists.
Can confirm
This may be true ... but have you tested this with a Van de Graff generator? 😁
Isn't there a large generator in the lecture theatre where they hold 8.02?
@@vinays1234 wtf man
I think u should try to focus on ur future like being a scientist or something else instead of doing videos on internet n wasting ur time follow a chemistry ideal women Marie curie who gave her 12 year life to research only on radiation n due to radiation died for our better future
@@ganpatikumarchoubey8878 I think you should let people follow their passion, and not tell them what to do and not to.
Good to know I’m stupid at any point in time
Woah look who's here
Have you taken a summer break?
Daily physics uploader...🙌
Thank you for suggesting physics book in your channel...I have bought almost all of your suggestions...
Nah boi, you’re killin’ it with your tensors👌
I hope Diana will get better soon! I had no idea she was featured on your channel!
I wish Diana a speedy recovery!
Most toughest exam is that for which you realise a day before that you have studied nothing
Well said
Or the one where, if out of 100 possible questions there are five you cannot answer, those five are the only questions on the exam ... even though you only have to answer any four out of the five.
Welcome to life.
One day (in university) I studied my whole week for a finance test on the day of the exam it was the human ressources teacher that showed up, my finance test was the next week ...
I thought my college biology exam was on Wednesday, but it was on Monday. I learned this when the teacher told us to put away our notes and binders. I somehow got a B on it, despite never studying.
A geometry exam without any shapes...
Chuckles
Im in danger
You speak the language of the gods!
@@InvinciblePepe he is talking about euclidean geometry
Rule in exam #1: Answer the questions, ONLY.
In this case, only points 4-6 need to be answered.
Using the information contained in 1-3.
4-6. No kidding. Astonish me. I can't wight. Or is that a weight of an unstable element. 4-6. Hmm . Are you changing me? Let's go smarty pants. U were saying??????
Whoa! Physics Girl + Tibees. What a dream-team ^^
I can’t believe you two actually collaborated. Thanks for listening to my suggestion Diana
Einstein, Newton, Diana and Toby.....All of them have two things in common. All of them studied PHYSICS & had/have LONG HAIR.
More than 2 though, they were all also infamously involved with the occult, and they were all interested in separating a technocratic master class from the rest of humanity... that is not these 2 girls but definitely Einstein, Newton, even Ben Franklin, Pythagoras, really anyone who was ever a key figure in this field
@@AJ0223Oh dear... You don't seriously believe this, do you?
These are two of my favorite TH-cam education-entertainment creators. You ladies are great!
Best wishes for Diana!
fustrum is a part (rather: portion) of a 3D solid between two parallel planes cutting it (or passing through it). it's what remains when some really bad person cuts away both ends of a bread loaf. :oP
In that case everyone loves to eat the frustrum of bread! Crazy, right?
Is it called the frustum because you're frustrated about not being able to eat the ends of the bread?
To me it sounded like a German word but apparently it's derived from Latin for "crumb", so you know I think you're bloody onto something with your bread theory.
@@Dractonis I assure you, 'frustum' is not even close to a German word. The German version would be 'Kegelstumpf' or 'Pyramidenstumpf' depending on what geometric body you based it on.
Wow😃😃😃 never thought you will Collab with each other. You both are my favourite TH-camrs and I am so happy to see you both in a single frame.
Please do more such Collab in future also
Great Video!! it was good seeing a older tests from one of my favorite technical and mathematical schools. Its interesting how simplistic mathematics was back then and how difficult and well fleshed out it has become.
Marvel: Avengers is the most epic crossover of all times
Me: watch this! - Tibees x Physics girl
I know that one, it's |Tibees| |Physics Girl|sin theta.
So good!
My first thought was that the problems are hard for us because we don’t know the foundation of an 1876 candidate and what he was allowed to assume. Then I realized that - yes, of course we know! Given the year, I suspect that these are all propositions from Euclid’s “Elements” (or at least some are) and the examiner want to see you reproduce the exact argument used by Euclid.
I solved most of them in school while preparing for IIT-JEE. The first problem has a nice name called the mid point theorem.
Yes a cooperation with Dianna! Love her channel!
Great idea for a video! Hope to see you two working together again in the future!
other youtubers: unboxing of tech things
*Tibees:This is what an 1876 MIT geometry exam looks like*
Although never a physics (or math) major I did know frustum. I must be very old.
A frustum is a pyramid or conic shape with the top section cut off. Most commonly used in APFSDS rods as the penetrating section
proud to say i understood all of these and was able to do the proofs as well. thinking i should have went to MIT :)
I went to Toulouse Institute of Technology. I'm not sure it's appropriate to abbreviate it.
Louis Francisco lol
Transire suum pectus mundoque potiri. Quoted from Luigi above.
Oh, i didnt know you did a collab! I hope the best for Diana.
Awesome to see these two great woman together in this video.
2:55 I've paused the video.
*1)* True.
*2)* True.
*3)* True.
*4)* By the Interior Angle Sum Theorem & dividing by 6, each interior angle of a regular hexagon is 120 degrees. An inscribed regular hexagon will have each of its interior angles bisected by a radius of the circle, producing angles of 60 degrees each. One side of the hexagon and the two radii intersecting it form a triangle. By the Interior Angle Sum Theorem & subtracting the 60s on the hexagon side, the angle formed by the two radii measures 60 degrees as well, thus the triangle is equiangular, which is then equilateral. Therefore, the radius is congruent to the hexagon side. QED.
*5)a)* Definitions: The frustum of a pyramid is the portion left after chopping off the apex with a plane parallel to the base. Lateral area is the combined area of the lateral faces of a prism/pyramid/frustrum/cylinder/cone; in other words, it's the surface area minus the base area(s).
*5)b)* Proof: The lateral faces of a pyramidal frustum are trapezoids, each with the same height, which is the slant height of the frustum. The lateral area would be the sum of all of the trapezoidal areas of each face. By the distributive property, the half-height of the trapezoid area formula can be factored out from that sum. By the associative & commutative properties of addition, the remaining addends can be rearranged so that all of the "upper" base lengths are together and all of the "lower" base lengths are together. The sum of the "upper" base lengths" is the perimeter of the "upper" base of the pyramid, and the sum of the "lower" base lengths is the perimeter of the "lower" base of the pyramid. Therefore, the remaining expression is one-half the slant height of the frustrum multiplied by the sum of the perimeters of the bases. QED.
*6)* The instructions state to skip problem 6, which is good because I have never heard of a "polar triangle" in any non-geography context. Based on the wording of the prompt, though, I would imagine it has something to do with reflection.
*7)a)* Cone: Volume = 20pi u^3, Lateral Area = 65pi u^2, Total Surface Area = 90pi u^2
*7)b)* Cylinder: Volume = 96pi u^3, Lateral Area = 48pi u^2, Total Surface Area = 80pi u^2
I've given 9th-graders who were bad at math harder geometry tests than this, & they almost all passed.
_Vocabulary on the test:_
Chord = A segment connecting two points on a circle.
Secant = A line which intersects a circle twice. (Contrast a tangent, which only intersects a circle once, & yes, the trig functions are named after these lines.) All secants contain chords.
Subtend = Painfully awkward term for "to separate a circle into arcs with a chord".
Intercepted arcs = Awkward but much more common term for "arcs bounded by these lines".
_Vocabulary in my answers:_
Apex = The vertex of a cone, or the vertex of a pyramid where all the lateral faces meet.
Addends = Things that get added together. (Compare "factors" in multiplication.)
QED = Quod erat demonstrandum, Latin for "that which was to be proven". Indicates that the claim has been reached logically so we're done with the proof now.
my name is Diana too ! and I love the geometry is my favorite subjet since I had 13 Years old !
thank u Diana y Toby
I think they might want you to answer “true” or “false” on the first question, accompanied by a proof of course.
it is badly phrased by modern standards. the command term "if" defines/supposes a statement, and therefore without a further command isn't really a question. It should have a prove or disprove in there somewhere
I suspect you are simply expected to draw the described forms in the first few "questions", to prove that you know the concepts and terminology.
I went to school in the 70's and the words arc, chord, subtend are very familiar words. I'm not sure if I know any words that can substitute them. A 'regular' pyramid is a pyramid that has all the sides of the base equal and the slant height of each face is equal.
Diana's jacket is really the most coolest things I have seen in a while...
Imagine going to give an exam wearing it...🤓🤓🤓
Nice to see Diana's smile and hear her laughter! So glad to see her on your channel!
This is now a regular class test of 10th class in India.
Bro end of class 10
It doesn't matter as much to forcibly remember the shape "frustum" as it does to have the insight into solving the actual problem.
This has been a learning moment. Thank you!
These questions are of M.I.T. 1856, but in present day these studied by the students of 9th standard.
Just consider it took 3 months to travel from New York to Chicago by horse or carriage. And you may die of dysentery or smallpox on the way.
I hope you don't mind saying, marvelous trousers toby!
Honestly I was wanting a collab b/w you and Diana a few days ago and this came to me as a surprise... Beautiful video! And the questions without any "question" was a new one... 👍🏻
A fustrum is a conic section and even the phone intelligence questions the word,, ignorant phone,, . A fez hat from Morrocco would be the fustrum shape. I think we say fez . With regards to questions about where's the question , well those slack days are today back with us with a number of errors occurred in the year 12 physics exam for HSC in Victoria Australia in just last few weeks .
On question 5 when you added up t1+t2+t3.... those are all equal because it's a regular pyramid. The top and bottom of the frustum are squares.
A secant is a line drawn through a circle thats not right through the centre. A trig secant is the reciprocal of the cosine ratio of triangle sides.
Why are our primary used trig ratios sine (o/h), cosine (a/h), and tangent(o/a) and NOT sine, secant (h/a), and tangent is lost to history.
(FYI: cosecant = h/a, cotangent = a/o, covering all 6 permutations)
Those questions are NOT talking about the centriod of the object BUT the bisects of each side.
( I also thinking, to bisects the base as it is one side of the shape and another side to find target frustum shape )
I know, late to the party, but I have a question. Could it be that question #1 was the instruction for how to cut the sides (4x) of the pyramid to create the frustum? Maybe they wanted the top perimeter to be one-half the length of the bottom perimeter. I think.
Slightly different way of thinking about question 5: Rather than computing the area of each trapezoidal lateral face, one can combine the faces to make a single parallelogram, and calculate that area. This way of intuiting imposes an extra step in the proof, but it's how I arrived at it ^^ Thought that was slightly interesting.
So, for the 1st question. You would label A as the left edge, B as the right edge D as the small bottom edge and D as the big bottom edge. We know that if triangles are similar then the ratio of their edges are equal: ((1/2)A)/A = D/C => 1/2 = D/C => D = (1/2)C. You can totally use numbers and variables! I wouldn't consider a verbal proof to be sufficient lol. Not trying to diss you, I definitely enjoy your content and respect you :)
Mann.... You're a perfect example of beauty with brains. 😍
It's crazy that I was taught about the frustum of a pyramid in 9th grade in Nigeria. I'd always assumed it was a commonly known word among scientists lmao
The questions sound like the same manner computer code is written, before they knew what computer code would look like if written out.
Please note the paper does say (for one of the questions) to look at the blackboard for directions. So it's possible further instructions were given.
Great to see historic test.
Would be great if you could get a historic exam from Cambridge Uni and see what Newton's exams were like. Or the oldest exams you can find...
Also my mom wasnt 'allowed' to study physics in a very elite highschool in 1950s because she was female. I assume MIT didnt have such issues in 1800s?
The first one is so easy , that use the intercept theorem . If you have a triangle ABC cut by this parallel line in points D and E then AD/AB=AE/AC=DE/BC and so ((1/2)AB/AB)=DE/BC so BC=2DE
The first question is taught in high school here..we call it Mid-Point theorem
The point is whether you see taught the proof
I'm really glad to see we still have some people that are trying to improve the education and level of thinking of others.
Thanks for everything:)
I love how the exam is just 'use Pythagorean and Thales' theorem' and some basic stuff but without telling you that you have to use them
Yahhh, you nailed it!
If you add "Specify the resulting geometric shapes and their properties (if)..." to the first two questions, you get a reasonably complex and sensible test of the student's understanding of mid-level Euclidian geometric concepts.
The first question is based on Thales theorem
To be more precise it is based on the Mid Point Theorem
@@kyusiv9026 that's what it is or you could say BASIC PROPORTIONALITY THEORM (B.P.T.)
@@blake2506 But mid point theorem is a Special Case of BPT that's why u have to mention it specifically
And Thales theorem is the original name of BPT
@@kyusiv9026 well
Feels to me like this is an oncomplete sheet. Like the sentences in the objectives relate to like a picture of an object or situation explained on a seperate paper
- I had so much fun (and confusion) with this video.
- I get the impression the first three statements were asking if they were "True" or "False", required the use of a drawing compass, and the student was being asked to scribe (show) their work.
- Note: #1 doesn't specify the type of triangle and it would be "False" for the scalene while "True" for the isosceles and equilateral.
- Notice how most of these questions could have a nautical navigation/cartographic application? I wonder how many applicants knew how to use a sextant?
Noone :
TH-cam : *Here's what an exam from 1876 looks like*
Did you watch only what you asked for? Obviously not. You arent clever enough anyway.
Coming from a Computer Graphics background, I encounter frustums a lot :D
Hey! I am not sure if I got it wrong but in the final problem, the first part, the lateral surface, 'h' was assumed to be Height and NOT Slant height, but in the second part, to prove its half the sum of both the perimeters multiplied by 'slant' height, it is still multiplied by the same value 'h'. Please feel free to let me know if I missed something. Was fun to see you folks do something interesting like attempting a centuries old exam paper. Cheers!
As as retired master mariner before the days of GPS, nay, calculators. We used astronomical almanacs, sextants and tables (Norie's and Burton's in the British commonwealth). Various functions of angles were tabulated to simplify calculations. The secant of x is 1 divided by the cosine of x. We also had the haversine of x which is 1/2 of 1 minus cosine x.
Also, I think that the polar triangle, in the question, refers to triangles drawn on a sphere. Spherical trigonometry, the basis of navigation.
It was long time ago and I might have dreamt it all.
I think the best mental mindset to be in, when watching these videos, is how can I ask better questions to get ahead not just in the test but life ...
I tend to think the first couple of questions are a kind of "draw this" to see if you can interpret the vocabulary correctly.
for #1 -#3 i believe they only expect a labeled diagram. your #5 def needs to mention the upper base is parallel to the lower. the prime notation for #6 means the A'B'C' is a transformation of ABC. just guessing, my math degree is from the '80's, before graphics calculators, and barely personal computers using floppy disks.
How am I 3 years late on this one ??? If TIBEES would age after all these years then I would be able to see which is new and which is a bit late.
Tibees must be travelling at relativistic speed, because it's apparent that time dilation prevents her from aging at all.
It’s so much fun and also so insightful to see physicists solve problems.
Brilliant online education.thanks for everything:)
I wouldn’t be able to get into MIT anyway in 1876 because my country didn’t even have math exam those times.
In the first problem, I think the answer could be that the triangle is an isosceles triangle. Or, perhaps this is a true/false question. I think the next two are true/false questions as well.
This shows the importance of knowing what words exactly mean. Once you have the definition of "frustum" the frustration stops and the question becomes accessible. I wish teachers and schools would pay more attention to definitions and dictionaries, also outside of MINT subjects. A textbook that uses terms before defining them is unnecessarily confusing.
frustums are used a lot in computer graphics as the plane of the camera (screen= top of pyramid) and then how far that camera sees (far plane = base of pyramid) and removing parts of object not within the frustum that cannot be seen. Wonder what they used them for in 1876!
These looks like the exercise I had to do in my first and second year of high school, we had math which was divided in algebra and geometry
I learned what a frustum was at school, but I next encountered the word while reading about the space shuttle's solid rocket boosters, where the frustum is the top of the booster where the parachutes are stored.
My reaction to an MIT exam -- run away as fast as I can.
The nosecones of the space shuttle solid rocket boosters are called frustums. They've been in plain slight for decades! 🚀
"Everyday Objects for $1000, Alex."
Hi @tibees I just love U're videos and the reason for it tat u Makin videos on different subjects (like physics , jee etc) which is quite unike and great keep up the good work. 👍
The first question was actually the statement of converse of mid point theorem . So you basically need to prove it
No picture on that exam gave me chills.
I just failed my hyperbolic geometry course :(...miss normal geometry stuff
Omg, Physics Girl and Toby collab!
Better crossover than Endgame
Goodness! another youtube colaboration! Love it.
Hi @Tibees, just a suggestion: use a mic filter or a sock to remove the sharp spikes in the audio. Your voice is really relaxing in most of your videos but the spikes really lowers the quality. Other than that, cute nerdy content that I will definitely want to watch more of. Thanks! :)
What's the most toughest exam in the world ???
Life.....!!!!
IITJEE
@@jitadipmukherjee3127 ca final
@@jitadipmukherjee3127 frankly I think on an average all the Indian entrance exam for institutes and civil services are way tougher than their foreign counterparts
@@jitadipmukherjee3127 UPSC : Hold my mains
Hi Valak
Glad to know that, as a high schooler, I could get a couple of these questions right.
Great video. Thanks Toby and friend 🙂.
Isn't this basic geometry ? I would love it if my all maths exams are of this level
Yeah bro..those are high school lvl geometry taught in india..
Duh it is. This is from 143 years ago. Very few people knew any sort of higher level formal math at that time. Knowledge is built on over time which ends up as us being taught this level geometry when we are ≤15.
It's a college *entrance* exam. I would expect it to be at the high school level.
Love this vid🥰
hope you make collabs with other physicists coz these are awesome 🙃
I've heard a few years back that a 1900's, like 1918 or something test was given to some college kids and they failed it miserably.
I think you were most of the way there on #1, Toby. I think they wanted you to make two more triangles on the bottom so that their two bases are each congruent to the base on the top triangle.
Is a polar triangle a triangle in polar coordinates?
Frustum is the shape which we see as flower pot and a bucket
Physic's Girl brought me here. Glad she did. :) New sub.
This style of just giving a statement and expecting you to prove it is common in mathematics textbooks.
A polar triangle comes from spherical geometry.
Yeah, as in Coxeter & Greitzer
4:13 i've heard those words too many times!
Line numbered one hints at the ability to take a triangle and bisect it in a way where you can then calculate the area of each portion towards then getting the sum of its total area. 😉 [ th-cam.com/video/lag22Hl2RQw/w-d-xo.html ]
You, physics girl, and veritasium guy are friends???
What do you mean
Diana and the veritasium guy are. Toby, I believe has just met Diana.
Ujjwal Kumar
They’re asking if these three youtubers know each other.
@@zain4019 OK thanks for telling
ah the two genders: physics girl and veritasium guy
In Italy we still use all of this terms, apart "frustum"