What are some real life applications of dilations?
828725
other examples of dilations besides the eye?  vascular smooth muscle relaxes allowing the diameters of blood vessels to enlarge.  sphincter muscles such as the anal, pyloric and cardiac sphincters of the gastrointestinal tract.  coordination of regions of the gut that dilate while more promixal gut regions constrict produces the phenomenon of peristalsis or movement of food through the GI tract.  The muscles around the trachea can be relaxed under the influence of the sympathetic nervous system to allow more rapid airflow into the lungs.  veins of the body are capable of dilation which makes veins potential reservoirs of blood.  Hope these examples help.  Have a great day.
882142
They exist, they are just not practical for visualizing 3D geometry.\n\nMost people have trouble with 1st and 3rd angle (2nd and 4th would be front and back "views" given a "side" projection).
548139
If you're talking about drops like Visine, the answer is actually yes.  If the drops have an antihistamine in them, dilation can be one of the side effects.  If you're wondering if the drops your using have that side effect, check the box or insert - it should say.
94315
To Improve Peoples Eye Vision
572521
Visine \nredness relief\n\n\n\n\n\nDO do drugs
644860
Lots of places, actually.  Algebraic number theory, Galois theory, linear algebra, discrete geometry, and other fields have shown tremendous usefulness in producing hard-to-break cryptography and digital signature schemes.\n\nAlgebraic geometry, abstract algebra, some real analysis, discrete geometry, linear algebra, Galois theory, and other fields are integral in the design of error correcting codes used currently in CDs, DVDs, satellite communications, your telephone and broadband lines, and many other places where reliable communication is needed.\n\nComputer science (I hope the applications of this are obvious!) essentially grew out of mathematical logic, with lots of influence from universal algebra and category theory.\n\nArtificial intelligence research also borrows heavily from several mathematical fields, most especially mathematical logic.  Though the true "thinking computer" is still science fiction, some of the results of this research is already used in word processors (including the dreaded "Clippy"!!!! but more useful places too), voice recognition software, automatic optimization algorithms for electronic circuit designs,  and other software, and don't forget the Roomba!\n\nAbstract analysis has solved many problems in fluid dynamics, with applications to aerodynamic design, electronic circuit design, Internet traffic management, and even road system design!  (Cars on the road behave a lot like fluid in pipes).\n\nLie algebras, tensor algebras, manifold theory, algebraic topology, systems theory, and several other abstract mathematical topics come into play with the General Theory of Relativity (GPS satellites take into account the General Theory of Relativity for their calculations--or else they would give badly inaccurate results!  Not only their motion, but the Earth's gravity has an effect on measuring time, which is essential to the process of geolocation) as well as quantum theory (which gave us the transistor, the laser, superconductors, and other current technology....and far more future technology) and very importantly, at least from an intellectual viewpoint, much progress on "how the universe works" fundamentally (we don't know for sure yet!).
354436
(m)\n\nField of View or Field Diameter is very important in microscopy as it is a more meaningful number than "magnification".  Field diameter is simply the number of millimeters or micrometers you will see in your whole field of view when looking into the eyepiece lens.  It is just as if you put a ruler under the microscope and counted the number of lines.  \n\nThe chart below will tell you (approximately) what to expect when looking through a microscope with varying combinations of eyepiece and objective lenses.  As an example (in green below), a dual power stereo microscope with 10X eyepiece lenses and 1X and 3X combinations of objective lenses, would have total powers of 10X and 30X and your field of view would be 20 mm and 6.7 mm respectively.  \n\nThis means that an object 20 mm (2 cm, or about 3/4 inch) wide would fill up the whole viewing area at 10X and an object about 6.7 mm wide would fill up the whole area at 30X.  As you can see, having the highest power may not be best for your particular application.  When you move to greater magnifications, you sacrifice field of view.
199983
See your eye doctor or go to the emergency room immediately!  Your eyes normally dilate together when exposed to dim lighting.  One eye dilating is abnormal and needs to be investigated.
794003
Any speed really will do. Even on modern day jet airliners the Time Dilation effect is measurable with very precise atomic clocks. Of course, its a very small amount, and you must travel at a significant fraction of the speed of light to experience a significant difference from a human perspective (e.g. at half the speed of light, the time dilation faction is about 1.15 (so time travels about 15% faster for everyone else than for you)). Though, to you, everything will 'feel' normal, as every atom in your body is experiencing the same effect. It's kinda weird (and by weird I mean awesome), but that's how it is.\n\nJust for reference here's the equation:\nt= t0/SQRT(1-(v/c)^2)\n\nWhere,\nt = the time observed in the stationary frame (say Earth)\nt0= 'proper time' the time in the moving frame (i.e. a spaceship, etc.)\nv=velocity at which the moving frame is moving\nc = speed of light
1051352
Drops for dilation are typically given in office in order for the physician to be able to see your retina. The are not an absolute must after retinal surgery and some physicians do not prescribe them.  It is not uncommon to keep a patient dilated in order to prevent added strain and further detachment on the retina which may be caused by the natural focusing of you eye when you use it.  Is your eye patched?  If so then I do not believe dilation drops would have much of an added benefit.  \n\nMore of a concern is your fever and pain and redness.  You should review your post-surgery instructions and if they indicate that you should watch for fever then a trip to the ER or urgent care clinic may be in order.  A post-surgical infection is NOT a matter that should be taken lightly.
196597
im taking AP physics B right now\nand i reccomend trying to make it interesting \nnot just saying the formulas bu relate it to things that people actually do, not saying "doesnt this remind you of relitive motion" but say "you know when ur driving in a car and the other car doesnt seem to be moving" things that people actually do
202857
Half-lives are part of the answer.\n\nIt is also used to compute the amount of energy absorbed by an exposure to radiation of this or that energy, of a given intensity for a given period of time.\n\nIt is used to construct the tables that tell the X-Ray technologist how to set up the machine (kV and mAs) to take chest films, hand X-rays, and whatever else: that's called Technique Charts.\n\nCT and MRI scanners use mathematical algorithms to generate the pictures they take--usually a version of Fisher & Tukey's fast factoring algorithm for 2 or 3 D reverse Fourier transform...  Yeah, right, that's a mouthful, and I hope I've got it clearly...\n\nThey used to use it to figure out how to move the X-ray emitter and the film to do plain old tomography, but on the whole, that's gone by the wayside since the advent of computerized tomography (CT)\n\nThere's probably more, but that's a good start.
392380
All kinds of simple, easy calculus examples in real life (especially engineering!).  These depend on the level of math knowledge, but for University Calc. II:\n\nOptimization: (i.e. give a box with a volume, find minimum surface area) or (here's a certain amount of fencing, make the largest enclosure you can).  (Lagrangian Multipliers? did I even spell that right?  We looked at those when there are a lot of constraints on the problem (i.e. relationship between box dimensions must follow .....).\n\nForces: for example, average fluid pressure on a dam, given a function of distributed force, or fluid pressure on a submerged object. (Can be done in single or multiple integrals).\n\nRelated Rates:  i.e. two cars approach at right angles, different speeds, when will they meet.  Or, dropping a ball near a light source, find speed of shadow as function of angle made with light source, distance from ground, etc.  Differetial calculus example.\n\nArea and Volume: Double and triple integrals to find the volumes and areas of shapes. (Or single integrals, volumes of revolution, areas from curve to axis, if multi-variable calculus not covered).\n\nCurve Fitting: really good real-life use, take a set of data points from an experiment, select a curve type (i.e. quadratic, cubic, straight line, logarithmic, etc) and use minimization to get the best curve fit (set up an equation for the residuals, sum of (function) - (data point), and take derivatives with respect to each unknown coefficient in the function, set all derivatives equal to zero, solve simulatneously for curve coefficients. Now we can predict the outcome of the experiment at intermediate values, (as long as the curve fit is good).\n\nCentre of Mass, Centroids, etc: Find the balancing point on certain objects or groups of objects using integration. Can be single or multiple integrals, depending on complexity of shape.\n\nFields:  i.e. graviational fields, electrical fields, etc.  Or make up some fields.  Integration to find work required by a particle to traverse a path through some field.  Conservative and non-conservative fields.  Can use as an example of energy needed to move satellites along paths (equations) in space near earth's gravity, an electron through an electrical field, etc.  I guess some of these examples the field is conservative and it becomes kinda trivial if you work with end points, but don't have to.\n\nThese are some of the applications we used in our Calculus II-type course.  The hardest part is always setting the problem up, not solving, (which makes for good application problems I guess).  If multi-variable calculus isn't covered yet, then some of these examples would be kinda rough (i.e. fields).  Anyway, hope these are useful. \n\nCheers,
730887
I have a pair of those interesting deep-dish-shaped double-domed parabolic mirrors from Edmund Scientific, the top one sits upside-down on the bottom one, and the top one has a hole in it.  So when you put something inside it, and move away at an angle, an image of the object appears to be sitting above the top dish.  I ask people, "Hand me that little pink pig sitting on that dish".  They see it, reach for it, pick up nothing, reach for it again, and see their fingers apparently pass right through a solid object.\n\nWhat is the reality there?  My eyes tell me there's a little pink plastic pig sitting on the top of that dish.  Yet when I try to pick it up, my fingers pass right through it.  But then I distort the mirrors a little, and the pig blurs in an odd way that lets me see that he's actually a reflected image from inside the unit.  And if I understand optics sufficiently, I understand that it is possible, with certain arrangments of parabolic mirrors, to erect "real" images (versus the more common "virtual" images that we see in most mirrors and lens) of objects, and even design and build versions of my own, with the effects and capabilities fully determinable in advance.  That's reality.\n\nReality does exist.  Granted, we have a limited and distorted view of it due to the limitations of our senses, but it does exist.  For example, this desk in front of me seems like a solid object.  But in truth, my view of it is limited by the fact that my eyes are not able to resolve the electrons orbiting the nuclei that make up the desk, and that the vast majority of this desk is vacuum, therefore the fact that, when I touch this supposedly-solid desk, what's actually happening is that the electrostatic field generated by the electrons of the desk are exerting a force against the electrostatic field of the electrons orbiting the nuclei of the atoms making up my fingers.  There are no "solids" touching anything, just fields pushing against each other the way 2 magnets can push against each other.\n\nTo me it looks like reality begins immediately outside your eyes.  All is reality.  The only place it ends is inside your head, when you misinterpret what your limited senses tell you.
482742
Micro electronics that you could see through. Nanobot technology. Using the contact lens as a focus lens. Tapping into the human body's natural electricity as a power source. Possible in a few years. \n\nIf the contact was a colored contact you couldn't see through, highly possible now.
818615
experimental tools and techniques used by him
557237
I have a camera mounted on a dissecting microscope that will do that.\n\nAlthough the resolution will continue to improve, pictures on a computer will always have pixels at some level of magnification. Using fractals you can create an image on the computer that can be zoomed in on indefinitely.\n\nAlso there is a limit to which light can resolve an image. Once you magnify beyond a certain range the wavelength of light is too big and you have to resort to electron microscopes. Maybe in the future smaller particles than electrons will be used to see things a small as individual atoms. At the moment we can see things as small as large molecules such as proteins and DNA.