<p>Guy, guys. It’s a Saturday night. Don’t you guys have better things to do on a Saturday night than CollegeConfidential? I know I do. Bourne Ultimatum is on (again). It’s better than this.</p>
<p>XRCatD in #55 is a long way there. However, mass is not thickness.</p>
<p>PEQ: Don’t kill yourself, it’s only a silly math problem.</p>
<p>The answer will, of course, be an approximation, an order of magnitude. So precise calculations are not necessary.</p>
<p>Stop stalking me.</p>
<p>1/16 " = 0.0015875 m
That amount is lost over 1.5 x 10^8 meters, or about 1.5 x 10^8 revolutions.
So it’s about “ten picometers” lost per revolution.</p>
<p>@ConCerndDad</p>
<p>MIT expects students to be able to solve Fermi questions with extreme precision? That seems a bit offbeat. Fermi questions require you to make assumptions about the givens, and I wouldn’t expect even the top high-school math/physics students to make all assumptions correctly.</p>
<p>The only way to solve this would then be through prior knowledge or through a set of assumptions that ultimately invalidates the purpose of mathematics, therefore you’re telling me that to be able to get into MIT, I must be able to abstract an extremely simple problem that contains one or more unknowns and to just guess at its value and ultimately assert its validity? Hey I get the whole point that you made about algorithmic optimization by abstracting the algorithm into its future form, however that’s the ultimate goal of computer science, not a luxury of the field, and the same goes with mathematics.</p>
<p>I think the point is to estimate so that you can check whether or not the real answer makes sense when it is actually measured. (ex: whether or not the magnitudes match)</p>
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</p>
<p>This is so funny
Every time I read this
I just laugh, laugh, laugh</p>
<p>Failboat: What ARE you taliking about. Sorry, it sounds like Techno-dribble. </p>
<p>Recharge: Fermi equations? Huh?</p>
<p>Try thinking simply.</p>
<p>Here’s a hint. Think about the problem again just before you leave the bathroom.</p>
<p>XRCat: does 10 picometers make sense? What’s a picometer? Could you explain that to an English major when you join the work force and he’s your boss in management?</p>
<p>(7-1.6)mm/((10,000,000/1.9)revolutions)</p>
<p>about 10^-6 mm.
aka
about 1 nanometer.</p>
<p>would you like me to explain what a nanometer is? -_-
sources.
[Walmart.com:</a> Tires: Do I Need New Tires?](<a href=“http://server1.kproxy.com/servlet/redirect.srv/sruj/shhzdcy/s1iwolzo/p1/servlet/redirect.srv/sruj/shhzdcy/s1iwolzo/p1/servlet/redirect.srv/sruj/scblyyol/snop/p1/cp/Do-I-Need-New-Tires/497361]Walmart.com:”>Invalid session)
[WikiAnswers</a> - What is the average tire tread depth on a new tire](<a href=“Invalid session”>Invalid session)
[Tire</a> Specifications](<a href=“Invalid session”>Invalid session)
[Schwalbe</a> Tires](<a href=“Invalid session”>Invalid session)</p>
<p>oh. and to answer OP question.
no. very few people are good at math. maybe 1 person per average high school that is even “decent” at math.</p>
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<p>I am referring to your little discussion about how the shortest algorithm is usually the more elegant solution. Trust me, the ability to produce the most efficient algorithm is not simply a luxury of computer science (and even engineering) but a requirement. At the same time, it is totally irrelevant to this situation because the problem assumes that we must know multiple factors in order to effectively solve the problem using a static set of equations, and if a single condition changes within the system, the whole system changes and your initial method for approaching the problem no longer works. For me, mathematics is the ability to produce a generalized solution without having to limit yourself based on a set of mutable restraints, if MIT expects otherwise, then I’m not sure that MIT would be the best way to go for any of us.</p>
<p>But then again, I’m assuming that pure mathematics is the way to go, not just a subset of it to be used in a practical environment, in which case I uphold academia over practicality.</p>
<p>Fermi question:
[Fermi</a> problem - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Fermi_question]Fermi”>Fermi problem - Wikipedia)</p>
<p>Lol guys. This problem is not representative of MIT/its expectations.
Also, we’re talking about a physics class…not a pure math class…</p>
<p>According to the questioner, the problem stems from the mathematical aspect of physics, and that absolutely no knowledge of physics is required to solve it.</p>
<p>If it were however a physics question, then one possible approach would be to look at the amount of heat dissipation that occurs per unit time (dt) and to integrate the product of that function (which is time dependent) with a coefficient that specifies how much rubber is lost per unit heat (dh/dt). Remember we’re working under the condition that we have no external sources to use, therefore we must only use the knowledge that seems to be common sense and can therefore can be estimated. The total lifetime of a tire in distance traveled is a much too large of a number to properly estimate (as the stability of your answer towards the actual answer will tend to deviate a lot), therefore only low number estimates are acceptable through rationalization, this gives us the ability to estimate the diameter of a tire (300 cm), the average speed of a vehicle during equilibrium (~35 mph on local, ~55 - 60 mph on a freeway), the weight of a car (~ 5,000 lb) and the percentage of heat dissipation towards total energy loss (let’s say somewhere between 10 to 20%). We also know that the frictional force exerted by the pavement on the rubber must have a coefficient towards the normal force of well above 1 for a good grip (else the car would just skid all over the place), and as it varies from tire to tire (pressure, age, etc), we can effectively replace the said coefficient with a lambda x where x is within the intervals (1,5). And now, we have all of the factors of the problem, and if any condition that relates to the problem changes, for example the bumpiness of the road, we merely readjust the affected variables and continue with the same approach.</p>
<p>Failboat: you are making things much too complex. Tires of cars typically do not slide on a road. Do your shoes slide on the floor? Same with a car’s tires.</p>
<p>I gave you a good hint: think of this problem next time you’re in the bathroom.</p>
<p>Exactly, in order to allow the tire to roll, there must be friction to prevent the tire from slipping, the heat dissipation due to the work done by this force causes portions of the tire to melt. I am of course discounting the attribution of the now increased viscosity to the friction as the recursive increase in friction will be sub-linear and therefore somewhat insignificant.</p>
<p>Now we can also simplify it (I agree) by thinking of it in terms of a roll of tissue paper, but the problem is that we can’t just estimate how long a tire will last (at least I can’t, or it’s not a common sense type of knowledge for me, as opposed to the weight of the car) therefore for me, at least, it’s not an intuitive approach to the problem.</p>
<p>I’m also working under the premise that we cannot use an online source to look up these values.</p>
<p>I wonder if the answer is just “zero rubber”</p>
<p>ConCerndDad: Why would my work force boss care how much rubber is lost per turn of the tire? The explanation of a “picometer” would depend on why he asked me the question in the first place.</p>
<p>Can we just have the answer please? The trying to find it game stopped being fun after about two hints.</p>
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<p>Can you give some examples of higher math problems that you are having trouble with? Also, what is the nature of your problem – do you feel you are missing some information that would help you come to a conclusion about a problem, or are you presented with all of the facts but don’t understand how a conclusion follows from them?</p>
<p>ConCerndDad’s recollection of his first programming assignment reminded me a couple of things I like to think about. Let’s say you are given an assignment to write a program that when given an input number, outputs the sum of all of the consecutive natural numbers up to and including that number (e.g. if the input is 2, the output is 1 + 2 =3). But this programming language does not allow you to use loops. Can the program still be written? You must justify your answer.</p>
<p>Another question, on a somewhat related subject. Which set is larger, the natural numbers (1, 2, 3, …) or the integers? Now given that information, how would you go about determining which set is larger, the integers or the rationals?</p>
<p>There was a rising MIT sophomore who wanted to take 18.100 (real analysis) and wanted to know if it would pose any problems. I posed the question to the student, to get an idea of the student’s background and interests. Professional mathematicians tend to think about questions like those (and also tend to take courses such as 18.100 when they are students).</p>
<p>I guess what I’m saying is that even if you are having trouble with this sort of thing now, it doesn’t mean that you will always have trouble with it. But you will have to spend a lot of time thinking about these types of questions. Also keep in mind that mathematics is a broad and growing field. No mathematician understands everything in mathematics. You might make breakthroughs in new areas of mathematics without having deep understanding of other mathematics branches.</p>
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<p>This is quite simple, let’s define the sumation function as phi(n), therefore, phi(n) = 1 + 2 + … n/2 + … n-1 + n. By folding in upon itself (adding the antiparallel strand), we can have 2<em>phi(n) = (n+1)</em>(n) ((n+1)+(n-1+2)+… for n times), therefore phi(n) can be re-expressed as (n+1)*(n)/2</p>
<p>C/C++/Java/C style languages:
int phi(int n) return (n+1)*n/2;</p>
<p>Python
def phi(n): return (n+1)*n/2</p>
<p>Lua
function phi(n): return(n+1)*n/2</p>
<p>etc etc</p>
<p>EDIT: I forgot to add in Haskell, the one language that doesn’t have iterative looping built in:</p>
<p>Haskell
addMeUp n = (n + 1) * n / 2</p>
<p>Although Haskell does allow list summation, which lets you do:
addMeUp n = sum([1…n])</p>
<p>
I admit, I had to look up the explicit definitions for natural numbers vs integers. </p>
<p>As natural numbers solely consists of the set [0, oo) where each element is an integer, and as integers include the negative of the set (excluding the duplicate 0), it’s obvious that (given that we’re solely comparing the magnitude of the set, and therefore the distance that the sets span) the integer set is larger as it wholey include the natural set as well as all of the negative integers.</p>
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<p>N ⊆ Z
|N| ≤ |Z| by monotonicity</p>
<p>Obvious is the most dangerous word in mathematics</p>
<p>Aren’t they both infinite, making none actually larger than the other?</p>