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Found 28 results

  1. Who thinks algeabra is useless i never seem to use it unless im in school
  2. And infinity doesn’t count . Mine is millinillion, but I also know what a googolplex is.
  3. What is your favorite school subject? Mine personal is art and creative writing.
  4. The Celestial Conjecture Abstract: In this article, we explore a question as old as MLP itself, one that traces back to the very first episode: How does Celestia and Luna raise the sun and the moon? We attempted this question using evidences from MLP episodes along with some of the most fundamental laws in physics such as Einstein's theory of relativity. Working with the assumption that the Equestria sun has similar propeties as the our sun, we made the argument that the Equestria sun has similar size and positioned at a similar distance away from Earth as the moon. We further propose the three celestial bodies, Sun, Moon and Earth are not in orbits with each other but stationary relative to each other. Finally, we conclude that Celestia and Luna raises the Sun and the Moon with their magic in the most literal way by positioning them above the land of Equestria during day and night respectively. Quantum Pony 1 1 Theoretical Pony Science, Pony Department The Institute of Pony Studies SW8 3AZ Equestria Introduction: (contains extremely minor spoilers from S02E11: Hearth Warming eve) Day and night in Equestria are brought magically by Celestia and Luna, and before that, by group of unicorns as shown in [1]. On the otherhand, in the world we are familiar with, magic is not required to bring forth day and night as it is achieved by the earth's orbit around the sun. Several questions are raised from this: Does the Equestria solar system follow the same heliocentric (earth around the sun) model as our solar system or does it follow a geocentric model (with sun around earth). Interesting and detailed discussions of this can be found in [2]. But a more important question is the role of Luna and Celestia. Is the whole "Celestia raising the sun" simply a huge lie to keep them in power and ensure no pony would overthrow them as it would endanger equestria itself? It is therefore the purpose of this article to investigate just how does Celestia and Luna raise the sun and the moon. Some Physics prelude: As stated in Axiom 2 of the previous entry, we will be assuming the laws of physics that works in our world works in Equestria universe as well. Although this does not mean there isn't new physics concepts in Equestria as well (which I am sure there are plenty). Luminosity: To investigate the question laid out in Introduction, we need to know the role played by the sun in order to sustain life on earth. As outlined in [1], the Earth ponies needs the alteration of day and night provided by the unicorns in order to grow food. It can be computed using the surface temperature of the sun, its radius and distance from earth the amount of power (per unit area) we receive here on earth. In our universe, this adds up to about 1380Wm-2 (where W is Watts, the unit of power). So the distance, d, the size, R, and the temperature, T, of the sun needs to be appropriate in order to provide that much power. Although the ponies may not need exactly 1380Wm-2 we will strive for something at a similar order of magnitude. The equation for the luminosity L (defined as the power per unit area) is: L = (some constant) x T 4 x R 2 x d -2 From this we can see the role played by inverse square law, basically, the closer the sun is to Earth, the greater the luminosity. So to have a large sun very far away is similar to having a small sun very near Earth (assuming they have the same surface tempreature T). Special Relativity: Now we turn our attention to the next topic: Special Relativity. Special relativity, formulated by Einstein, is one of the greatest achievements in the 20th century. It gives rise to what is arguably the most well know equation: E=mc2 . But there is another consequence of special relativity, one that is even more important and controversial in the old days: Nothing can travel faster than the speed of light. This is arguably one of the most firmly established and tested law in physics and we must assume it to hold in the Equestria universe as well. Otherwise, we will not be able proceed at all with any form of physical theories after Newton, and assuming faster-than light travel causes a lot of problems with causality as well. Hence, we propose the following: Theorem 1: Magic is a fundamental force of nature. Corollary: As any other fundamental forces of nature, Magic cannot travel faster than the speed of light (300,000km/s). The Equestria Solar system: Position of the Sun, Moon and Earth: In our universe, the moon is positioned dmoon=4x108 m away from earth with a radius of Rmoon=1.7x106 m. On the otherhand, the sun is positioned dsun=1.5x1011 m away from earth with a radius of Rsun=7x108 m. The position and size of the sun gives the correct luminosity to sustain life on earth. One interesting property is that the ratio Rsun / dsun is approximately equal to the ratio Rmoon / dmoon . Infact, this is the reason why the moon and the sun looks the same size in the sky! The importance of this in our investigation will be obvious soon. In [3-4] there are several incidences where the sun is raised by Celestia. One of the most important thing to notice is that as Celestia raises the sun (the moment her unicorn shines bright with her magic), the sun immediately moves as well. But if the sun is at a distance 1.5x1011 m we know it takes about 8 minutes for light to reach the earth. Hence, her action of immediately moving the sun (which if counting her magic reaching the sun and the light from the sun to reach us, should take 16 minutes) would violate Theorem 1 as stated above. To ensure special relativity and hence causality to hold, we need a sun much closer to earth for what happened in [3-4] to make sense. From [5], we can directly compare the size of the sun and the moon in the sky and it shows they are approximately equal, similar to our universe. So we have two conditions to meet: Condition 1: The sun must be near enough to almost immediately react to Celestia's magic Condition 2: Its luminosity must be such that it can sustain life on earth and appear as the same size as the moon. Miraculously, both of these conditions can be met! Proposition 1: The sun is just as bright as ours but has the same size of the moon and placed at approximately the same distance away from the earth as the moon. This is near enough for Celestia's magic to cause an immediate reaction of the sun (with about a 2.5 second delay) and bright enough (~1380Wm-2) to support life on earth. Hence explaining the scenes in [3-4] as well as not violating special relativity. Of course, we can place a slightly larger sun slightly further away as well and still meet Condition 2, however, we need it as close as possible in order for Condition 1 to hold. Furthermore, due to the possiblity of an eclipse, the lower boundary on the distance is that it still needs to be further away than the moon. The actual movements of the Sun, Moon and Earth: When two celestial objects such as the sun and earth comes near each other, they will be caught in each others' gravitational pull. As a result, they orbit around each other, with the heavier body appear more still and the lighter one appear to move around it. This is how planets orbits the stars and moons orbits planets in our solar system. However, one of the reason this works is that out of all the fundamental forces, only gravity is significant in this situation. Equestria on the otherhand, has another significant force which is Magic. The ability of Celestia and Luna to move the sun and the moon shows this long range force is significant enough to combat gravity. Hence, it wouldn't be a surprise that the even though planets might orbit around each other before the time of ponies, when the unicorns came they stopped the orbit with their magic. As a result, one can make an educated guess that the sun, moon and earth are stationary relative to each other. Now lets get into some more detail. There are times in [5-6] where there is no one to perform the duties of raising the sun and the moon. If we consider the above theory that unicorn magic is the force that repels the gravitational attraction of the three celestial objects, wouldn't they collide into each other during its absence? The answer is yes. However, due to their distance apart, it would take a significant amount of time for this to occur such that in the time frame of [5-6] there wouldn't be a significant difference in their positions in the sky. This can be computed using Kepler's laws and the result is about 5 days. For more information see [7]. With these features established, the act of Celestia and Luna raising the sun and the moon is exactly what it is. They used their magic to position the sun and moon above equestria to create day and light. At night, the sun would be rotated to the otherside of earth and similarly for the moon during the day. Questions yet to be addressed: The propositions above solves some of the questions but also raised some more questions. For a star to be the same size of our moon is unheard of in our universe and seems even more difficult for it to be just as bright as our sun (since it needs to be at a certain size to sustain the fusion reactions in its core). Furthermore, the mean density of the moon is lower than that of the sun, hence for them to be the same size, the moon would probably have been heavier thus contradicting the comments made by Celestia in [8]. However, the above calculations maintains that the sun merely have to be approximately the size and distance of the moon. We can place it slightly further away, with a larger volume and lower surface temperature and still allows the same luminosity to sustain life on earth and keeping laws of relativity intact. Although the exact computations needs to be worked out. There are also questions about whether the Earth is flat or spherical. My personal view point is for Earth to be spherical and such arguments were already made in [9]. However, a flat earth Equestria would not significantly hurt the arguments above as gravity still works the same way. Celestia simply needs to take the sun to the 'backside' of earth. See [10] for a visualization of this process in a different universe. Conclusion: The position of the sun can be chosen to be approximately the same distance away from earth and with the same size as the moon. This allows a luminosity that can sustain life on earth as well as not violating the laws of relativity when Celestia uses magic to move it. Furthermore, the sun, moon and earth are stationary relative to each other instead of being in orbit. As a result, Celestia and Luna raises and lower the sun and the moon by using their magic to resposition them above the sky of Equestria and thus bringing forth day and night. Future work can include doing some more computations so that the numbers adds up and considering other effects that a smaller and closer sun could do to Equestria. Acknolwedgements: Quantum Pony is grateful of all the insightful and stimulating discussions in mlpforum and fimfiction. Quantum Pony is supported by the Equestria Potato Grant. References: [1] Williams, M et al. (2011) S02E11 MLP:FIM [2] Batbrony et al (2013) The Solar System of MLP: Ptolemaic or Copernican? mlpforum [3] McCarthy, M et al. (2013) S04E02 MLP:FIM [4] McCarthy, M et al. (2014) S04E26 MLP:FIM [5] McCarthy, M et al. (2013) S04E01 MLP:FIM [6] Haber, J et al (2016) S06E25 MLP:FIM [7] Scileander et al (2017) If you were to fall the the distance that the Moon is from Earth, how long would you fall? [8] Lewis, J et al (2017) S07E10 MLP:FIM [9] Ponitten et al (2016) A theory that could prove that Celestia doesn't raise the Sun after all, mlpforum [10] Summit Entertainment (2016) Gods of Egypt
  5. Math guys, I like some help with this. I might do it for a future story. So, how big would Princes Celestia be if the average pony was the size of a shire horse?
  6. We also put way to much thought into this. I thought this would be complex algebra, but it just turned out to be simple geometry. I have known how to do this since 6th grade.
  7. In the IDW comics, Pinkie Pie has unveiled that she carries live ammunition for her party cannon. She has attempted to do that even NOT AS A VILLAIN, against Iron Will. Thankfully Rarity stopped her, otherwise he'd be dead! I decided to do a few hours of speculation as to consider how powerful her cannon 290mm deliverer of fun actually is! Conclusion: she could destroy any modern tank, as her cannon is about the strength of one found on a WW2 era battleship
  8. In this short entry, I will try to list of the Axioms or fundamental principles that we should follow in order to investigate the scientific laws in Equestria. Most of the science we encounter have two main branches, Theoretical and Experimental (there is also computational but not sure how we can investigate that in Equestria given computers doesn't really exist there...) . Since we cant really carry out experiments (as we do not live in Equestria), we can only investigate evidences that are presented in MLP episodes. And our job is try to explain these phenomenons and formulate a complete picture of science in Equestria. Axioms: Axiom 1: Anything in the Equestria universe displayed in an episode / movie are considered to be Facts. Note on Axiom 1: We should not assume all scientific theorems that works in Equestria universe works in Equestria Girls universe. But this does not mean they don't overlap at all given that they can travel from one universe to the other. Axiom 2: Scientific theorems and laws that are true in our universe is also true in Equestria universe. Note on Axiom 2: For example, we can assume Newton's laws of motion to be true in Equestria universe as well. Although there can be scientific laws in Equestria that are absent in our universe. So to be more exact, the laws of nature in our universe forms a subset of the laws of nature in the Equestria universe. This is the least number of axioms I could think of in order for us to proceed. Hopefully we won't need more in the future but we shall see . Next entry: Lets test things out
  9. So I have been getting frustrated about what 0/0 is, so I made a C++ program that will divide 0 by 0 and this pops up as an error this was the code ; so I decided to input the 0s in manually, and if I try to divide 0 by 0, the program fucking crashes here is the source code to try it for yourself ; ; ; and I found a physics forum and they didn't have a clear answer (or I'm just dumb) https://www.physicsforums.com/threads/zero-divided-by-zero.29213/ does anyone know the answer to this major black hole???
  10. Because I like to do numbers (calculations will be done to the 6th decimal (hundred-thousandths), while displayed values will be round to the 2nd decimal (hundredths) or 3rd decimal (thousandths) for clarity's sake. Also, assumptions are made that measurements mentioned or shown in the show are calculated from Equestria to Earth Imperial for the sake of simplicity on the viewer. Much like how they speak English instead of whatever Equestria horse language they have. In Hearth Warming's Eve we get an off-handed mention of an "eight-foot candy cane" which has a young foal beside it. Working off that, the candy cane is 243.8cm tall, and 210px tall. Thus we've learned for that one scene 1 pixel is 1.16cm. Using that scene we can measure a foal in MLP is 34 pixels tall at the withers. The head itself is 57 pixels from top of the head to the ground, and the x-axis (length) of the body is 27 pixels. Thus: Foal: 34 * 1.16 = 36.47cm (1' 2'')at the withers, 57 * 1.16 = 66.17cm (2' 2'')tall, 27 * 1.16 = 31.35cm (1' 0")long torso. From here we can take a scene in Stare Master where the CMC are exploring Fluttershy's cottage. There is a moment where we have Scootaloo standing next to Fluttershy, allowing for a comparison. In this scene Scootaloo is 122px tall, leaving a pixel being 0.54cm. We can also measure the front view of a foal and determine that a pony's head is spherical. Fluttershy is 202px tall, and the angle of the “camera” to the pony allows for measuring her height, z-axis of her torso, and both the diameter width and y-axis of a leg. Pony: 202 * 0.54 = 109.57cm (3' 7") tall from hoof to head, 45 * 0.54 = 24.30cm (9 9/16") wide torso across the z-axis, 81 * 0.54 = 43.74cm (1' 5") length of a leg, 25 * 0.54 = 13.50cm (5 5/16") width of a leg. Jumping scenes, lets swing over to a Bird in the Hoof and grab a shot of Fluttershy and Princess Celestia together. The “camera” in this scene allows us to get both the y-axis and x-axis of Fluttershy's torso, the diameter of her head; and the x-axis of Celestia's leg, the diameter width of Celestia's leg, her neck's diameter width and y-axis, and both the y-axis and x-axis of Celestia's torso. The scene is working off of comes out to be 1px = 0.676 Pony: 62 * 0.676 = 41.91cm (1' 4") torso x-axis, 36 * 0.676 = 24.34cm (9 7/16") torso y-axis, 54 * 0.676 = 36.50cm (1' 2") head diameter, π * (25 * 0.54 / 2)² * (81 * 0.54) * 4 = 25,380.66cm³ volume of all four legs, 4/3π * (62 * 0.676 / 2) * (36 * 0.676 / 2) * (45 * 0.54 / 2) = 13,048.66cm³ body, 4π * (54 * 0.676 / 2)³ / 3 = 25,508.02cm³ volume of head. Using a sum for the total volume (63,937.35cm³) and the average density of an equine body (999.958 kg/m³), we find out that an average pony weighs in at 63.94kg (141lbs). I have other findings regarding pones, but they don't fit the board's ratings. Let's just say you're too big for your pony waifu. Also, a human in Equestria would become famous at the bars for the ability to hold down drinks. If we compare the numbers derived from these calculations to numbers derived from other means (such as the spoiled image below, where ponies are compared to apples, clocking in at about 40") we find the 3' 7" matches quite well with expected standards calculated above. This leaves a single discrepancy in the show: Rarity saying the heart-shaped ruby Spike finds to be at least 20 carats. Using Earth standards, that ruby is closer to 2000 carats. If the ruby was actually 20 carats, then ponies would be about as large as the actual toys. With base calculations out of the way, we can start to figure out the physical measurements of any character by comparing them to one another. For the sake of presentation, calculations and will be posted at the end in spoilers. Equestrian Ponies average mare: 41.91cm by 24.34cm by 24.30cm , 63.94kg average stallion: average foal: Big McIntosh: Princess Twilight Sparkle (G4): Princess Twilight Sparkle (G5): Princess Mi Amore Cadenza: Shining Armor: Princess Luna: Princess Celestia: 66.25cm by 26.36cm by 28.32cm , 87.74kg
  11. I was arguing with four of my friends yesterday about our favorite classes in high school. After deciding American History is best history, we started arguing about science. Anyways, I know everyone hates science and that science is stupid. But I'm a bio major atm and I have to think about this all the time. My personal favorite was astrophysics, followed by physics. HPA was okay. I know, maybe I should have majored in physics. Still have time to switch. While I'm at it, I'll just include best math class. I hate math, but I figure why not. Unfortunately, my school only offered up to Calc 3 so I had to waste a year with AP Stats, which was full of stoners. Not pleasant. Algebra 2 was my favorite, because my teacher was a boss. TL;DR Vote for your favorite
  12. You know when you're fooling around on the calculator and you get a strange error. You either tried to find the square root of -1 or divide by 0 The square root of negative one is just the letter i if you were wondering , but you see I think that the reason you can't divide by 0 is a simple problem with the way dimensions are perceived. Try representing a line with one point; it doesn't work! Don't understand? Don't worry...it's very complicated. However the solution is simple if you realize what is actually happening. I believe that when you divide by 0 you are essentially adding a dimension! Points become lines, lines become planes, and so on. I probably wrong so don't get your hopes up. :comeatus:
  13. I published this story on fimfiction a while back, but forgot to mention it here. Twilight Sparkle proves she can win a race against Rainbow Dash. All she needs is a tiny head start.
  14. Hey there! Here is Lemon Slices, with my first forum game. Since there are many counting threads, I suggest another one, more challenging in the long run. It is simple: Pick the number from the user above, double it, and post! Of course you can post another things within the number (Obviously respecting the Global Rules), but the number you are posting is the thing that really matter. Let's start: 2
  15. Don't freak out, I'm not gonna use numerology here, just science I'm a Unicorn, and mathemagic is my favorite branch of Magic. But I use to see that most humans tend to hate it. To change its bad reputation in your world a little bit, I decided to play Trixie and show you some cool mathemagical spell I learned recently when studying some old books by Starswirl the Bearded. OK, so here's the deal: Tell me your... favorite number (or your lucky number if you wish), and your... birth date (in a YYYY-MM-DD format, unless you prefer it written differently), and in return I'll tell you some Magic NumberTM. Then, when you raise your favorite/lucky number to the power of that Magic Number, the result will start from your birth date (when you put down its decimal digits). Here's an example of what I mean: My favorite number is 7. My birth date is 1982-12-03. The Magic Number is then 1316831, because 71316831 = 19821203202357042996...2076482743 . The actual number has 1112852 decimal digits (over a million!) so I didn't put down the entire number here, just the relevant part, contracting the humongous rest into the "..." in the middle. Now it's your turn to experience the Magic Do you want to know your own personal Magic Number? Then just post your birth date and your lucky number here in this thread, and once a couple of posts I'll post your Magic Numbers here. Or, if you don't want to disclose your birth date in public, you can send me a PM as well, and I'll send you your Magic Number back. (I just hope I won't get flooded with PMs, and there will be at least a bunch of people who will post their birth dates here for the sake of public performance of Magic ) Of course you don't need to believe me on my words. Please feel free to verify that what I'm telling is true. You can do it with Wolfram Alpha by typing in: 20 digits YourLuckyNumber^YourMagicNumberreplacing the camel-cased words with the numbers I provided you, of course. This way you can check the first 20 decimal digits of that power of your lucky number. See? Told ya mathemagic could be fun Who would guess that your entire birth date can be found in a power of your lucky number
  16. Hey there everyone! There is a new game on the horizon, "No Man's Sky", and it's looking to be one of the most anticipated games of 2014. Procedurally generated, the game promises an infinite play space with billions of planets to discover. The focus seems to be on a classic sci-fi, wonder, and exploration, showcasing vibrant colors and diverse flora and fauna. Here is the reveal trailer: Personally, I'm extremely hyped for this game. The technology of the procedural generation is groundbreaking, and the ambition is commendable. I'm extremely curious as to what my fellow forum users think of No Man's Sky, and if you have any questions about the game I'll answer them to the best of my ability.
  17. Okay, so I noticed something in Hurricane Fluttershy. Rainbow Dash's goal is to get over 1000 wingpower for the tornado. However, at the time they need to make the tornado to transport the water, they're in danger of not having enough wingpower to even lift the water (800 WP.) This kinda doesn't make sense. The idea is that each pony needs 10.0 WP in order to beat 1000 WP. This would mean that if every pony were flying at 10.0 WP, there would have to be at least 100 ponies. However, there are 8 pegasi out with the feather flu. This would mean there are, minimum, 92 ponies. If they're flying with 10.0 WP, they'd still have 920 WP, which is plenty to lift the water. Heck, it would even still beat Fillydelphia's record of 910, which is what RD was really looking to do. I suppose it's possible that not everyone is flying with 10.0 WP, but at the same time, we saw that some ponies were flying with more than 10.0 WP, like Rainbow, who had 16.5 WP, and that was before training. There might also be fewer than 100 pegasi, total, but that would mean that they'd need more than 10.0 WP each in order to break 1000, and RD said that 10.0 WP would be enough for each pony. I can't ascertain the specifics 100%, but any way you slice it, it just doesn't add up. They would have to have made the number of sick ponies a lot larger in order to have it make sense. Around 20 would probably have been best. This would put them at 80 ponies, flying at 10.0 WP, would put them just at 800 WP, but it would still be believable, because it's still possible that not everypony would have had 10.0 WP. Anyway, this is a real nitpick, but it's always sorta bugged me. What are your thoughts on this? Does this make sense, or no? Is this believable or not? Do you have your own explanation? Let's discuss.
  18. I've seen recently several threads appeared with different kinds of questions, more or less serious/strange/etc., but I guess all simply coming out of curiosity. I asked some myself, too. (Guilty.) This has got me an idea: I bet anyone of you has some nagging questions, which you carry in your head since long time, and no one ever could answer you to them. Right? E.g. why is there that white crayon in the crayon box? Or why is the sky blue at day, red at sunset, and black at night? Or why are we being forced to remove irrationality from the denominator of our fractions in math classes? Or where do we know the digits of the number pi from? Or why is the heat flowing from hotter to colder objects and not the other way around? Or what is time anyway? Or how can a high-jumper jump higher than his own height? Or why are some thick objects transparent, when some other, thinner object are not? And lots & lots of other questions, I guess... But I also noticed that many of these questions I can answer (I'm a smart pony after all, if you didn't notice ). And I guess that many of you could know the answers for some other people's nagging questions, too. So why don't we just make a bargain? I like solving problems, and I'm unstoppable in my drive for knowing the answers. This way I found (or discovered) answers to many of the nagging questions from my childhood and adult life. And many people come to me and start asking more questions as soon as they notice I can answer them. That's why I'm curious of your nagging questions. What bothers you from your earliest childhood to this day? Do you have some questions which no teacher in your school could answer? Or something you always wanted to understood but no one could explain it to you in a comprehensible manner? (People tell me that I have a talent for simplifying things and explaining in a comprehensible manner, so you can count on me ). Please ask your questions here in this thread. And if you see a question of your peer you think you know the answer, feel free to help your friend I'll try to answer them too, if not here, then I'll try to write a whole article about that on my website if I find something interesting enough (There are some interesting articles already you can check out. E.g. about solving quadratic equations in your head, using simple geometry instead of the dreaded quadratic formula.) What do you think of this idea? And don't forget to post your nagging questions
  19. Ok guys, for those of you who are mathematical (Like me) Can someone look at this and tell me what's wrong with this? Apparently 3=1 in this equation. Sorry if its illegible, i have bad handwriting. I know this is not possible, but this equation makes my head hurt. Can anyone prove this wrong? XD
  20. Who else is in the FRC?(First Robotics Competition) I was wondering so I could find people at competitions and chat with them. If you are, what's your team number and stuff. I'm from 5041, System Overlord Robotics.
  21. All right from studying for finals coming up I had an idea to make this thread. So what is that one class in school where you're just like, "I just don't get it." For me, it's Honors Geometry because I'm more of an Algebra person, and Personal Finance, which is where we learn to deal with money and taxes and stuff. That class is like gibberish to me. So discuss away
  22. Goddammit! Pinkie I'm trying to do my work. Just a little doodle I drew while doing some trig work. criticism is welcome, just don't be too hard on me.
  23. Hi everypony, I'm going to try to make this short... I still have a lot of work to do tonight and it is already past 2 in the morning. I am certain that this thread, which I have aptly named "Mathematical Nerds?" will turn into a bit of a rant for some, while those who aren't quite as mathematically inclined (not that that's a bad thing, I am quite jealous of the writers, artists, etc. in the crowd!) may look at with disgust, but after certain consideration I have decided to see to it's conception. As such, a brief explanation of the sole purpose of this thread is in order: This thread is to enable those of you who have quite nerdy, mathematical lives, to vent about the irritations that one might come across when discussing mathematical concepts in one's daily life. It also is to discuss mathematics at any level, or share any opinions on the matter (ie. do you like math? hate it? etc.) Don't feel a need to read my huge rant below btw. it's full of irritation and frustration, and not much that is good. But if you want to read it, please do Some of you may have some similar stories too. Without further ado, let me begin with the first (and perhaps only) rant on the matter... The discussion begins to a point my freshman year of college while happily walking back to my dormitory. I overhear the kids in front of me talking about some mathematical concepts, which I believed to be related to my multivariable calculus class or perhaps my course on differential equations. Anyway, my ears perked up being the math nerd that I am and to my horror this was what I overheard: "... and then you just use Yuler's method for...". I don't quite recall what the actual topic of the conversation was, but I presume something like that. Regardless, the students butchered Euler's name. For those of you who don't know, Euler is pronounced "Oiler", not "Yuler", and this, I'm sure, a source of great discomfort for professors in mathematics and related fields. Considering Euler is one of the greatest and most influential mathematicians ever, it's rather shocking to hear his name pronounced as such at the collegiate level, let alone a prestigious technical institute, where it seems Euler's name comes up in almost every class offered. Now, fast forward a couple years, and we get to my Junior year of college. I look at one of my homeworks, which asks me to take the Jacobian of a quaternion. This baffled me at the time (and still does to some degree... Never quite grasped quaternions), so I asked a friend who was enrolled in a computer graphics course and is, as such, exposed to quaternions on what I would imagine a near daily basis. She looks at it and says, "Oh, yeah, I mean I know what a quaternion is, but a Jacobian of a quaternion? That doesn't make any sense. I know what a Jacobian is, but you can't take a Jacobian of a quaternion." To that I ask, "Do you know what a Jacobian is?" "Yeah, of course. It's like that 'r' and such that you multiply when doing coordinate transformations." Table flip. Sure, Jacobians are useful for coordinate transformations. Also, it might be partially my own fault for not clarifying, but the problem, which just said to "find the Jacobian of the quaternion" should have made it clear that it referred to the Jacobian matrix, not the Jacobian determinant. I believe this to be an example of mathematical incompetence of a rather annoying sort; the assumption that because one understands a single use case of a concept, or has seen a term thrown around by a couple equations or a term, that one fully understands the concept at a deep level. I don't mind a lack of mathematical knowledge. I know that there is a lot that I don't know myself, and I also don't feel I actually understand most of what I can blabble off. But what does get to me is the cocky attitude that one understands the concept fully, when one has clearly only seen its use in a limited scope. Alright, I just wanted to get that off my chest, and I'd like to open the floor up to all sorts of interesting mathematical discussion
  24. So, recently I was bumming around here, and there was just a quick query which somepony posted. They were asking simply “How long is 100 Moons?” At first, I thought it would be very simple to answer. In any media which I’ve read where animals are the main characters, “moon” has always been the standard measurement of time. In Watership Down, Warriors, The Sight, and MLP, “moon” has been the unit of time, because non-humans would obviously stick to things more easily observable than the orbital period of the Earth around the sun. Standardly, a “moon,” or Lunar Month, is the length of time form one New Moon to the next. It is usually around 28-29 days, but it varies. So, I did the multiplication, and calculated 100 moons as roughly 2,900 Civil Days, or 8 Solar Years. But then it occurred to me. I was using values from our Universe, from our solar system, and our Earth. Not every moon or planet orbits at the same rate. And in fact, Equestria’s sun and moon don’t even orbit in the traditional sense. They do not move of their own accord- the Celestial Sisters move them. And that leaves an interesting idea to be considered. How is time measured in Equestria? How does astronomy even work there? With a geocentric model of the solar system where things don’t move on their own, everything we know about planetary dynamics ceases to apply. And this leaves us viewers at a loss. We are now dealing with a system that functions completely differently from anything we know. So, we need to try and use only in-show evidence to make a determination as to how Equestria functions as a natural system. We do have some safe assumptions we can make. The Equestrian solar system is geocentric, with the sun and moon going around the planet (shall we call it Equus?). Equus’ axis of rotation must be slanted with respect to the orbit of the sun and the moon, because otherwise there would not be a polar ice cap. Days do vary in length as the year progresses, since there is a longest day of the year (The Summer Sun Celebration). There is some level of a natural progression of the seasons, since leaves turn colour on their own, implying that winter would come, ponies or no. The ponies simply make the transition between seasons move quicker. So in most every respect, Equus seems very much like Earth. For our purposes, the assumptions above will be what we work with. As a system, we cannot apply logic to Equus, or the question here, if we bring up the notion of the Celestial Sisters raising the sun and moon. For our purposes, we need to assume here that the sisters move not the bodies themselves, but the planet Equus, because it just doesn’t work if we have them pushing the bodies in an orbit around Equus. There’s a reason the Geocentric model failed. If the we accepted that the sun were pushed around Equus, and not Equus around the sun, a year would be the same length as a day, and seasons wouldn’t exist. We will pretend that somehow Equus is in a geocentric system, and somehow it acts as if it is in heliocentric system, because this is what we see based on the observations we made above. That being said, let’s move on to the bigger issue here. Time. How does it work in Equestria? We know that the ponies measure time in moons. How long is a moon? Well, we can’t tell based strictly on information in Equestria, since, as we see above, our logic does not apply to it. So, let us turn to the human world. Yes… we are consulting Equestria Girls. *yay* In EQG, the mirror opens every 30 moons, Equestria time. 30 moons in Equestria is equal to roughly 3 years in the human world. We know this because Sunset Shimmer has spent 3 years in high school, and a high school uses the solar calendar. The human world, we can assume, functions exactly as our world does. There is no magical, physics-defying nonsense. So we know that 3 years in EQG (or our world)= 30 moons in Equestria. Now we can do simple math to find out the length of an Equestrian Moon in our time. Get Derpy if you’re nervous. 30 moons in equestria = 3 earth years. Divide the whole thing by 3 to find out how many Equestrian Moons are in 1 Earth Year, and the answer is 10:1. Every 10 moons in Equestria is 1 Earth year (EY). Now, let’s do another step to find out how many earth days are in 1 Equestria Moon (EM). One Earth Year is 365.24 Earth Days (ED). So, 365.24 ED= 10 EM. If we divide the whole thing by 10, we get 1 Equestrian Moon is equal to 36.524 Earth Days. So, now we have something to work with! Using this information, we can get a scale of how time flows in Equestria. The moon orbits Equus at a slightly slower rate than our moon orbits us (remember, Equus acts like it is in a heliocentric model, even if it isn’t.) So, to answer the person’s question on the forums. 100 Equestrian Moons is equal to 3652.4 Earth Days, so 10 years. What do you guys think? Did my math bore you? Or do you find this interesting knowledge which helped you learn about Equestria? Did you note any flaws in my calculations? Let me know what you guys think!
  25. Based on the math and science (which im not going to do, its summer break) do you think that it would be possible to perform a sonic rainboom? We know that jets can perform a sonic boom, but what makes the rainbow effect of the sonic rainboom? Could we actually replicate a sonic rainboom?