Gold Nanoparticle - Sixty Symbols

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  • Опубліковано 1 січ 2025

КОМЕНТАРІ • 389

  • @ObjectManipulator
    @ObjectManipulator 12 років тому +3

    The first one was "A cow to a physicist is basically just a large sphere, sometimes you consider the tail, sometimes you don't." And his analogy for the size of one quintillion was "You'd require a 20 meter deep pile of Maltesers, which spread out over an area the size of Ireland" Hope that helps! :D

  • @rioross
    @rioross 12 років тому +2

    I've only had those chocolate candies on his desk once in my life. They don't sell them here in Minnesota, or anywhere in the US, but I can tell you, they are absolutely fantastic.

  • @RavenMad101
    @RavenMad101 11 років тому +2

    So Cool, You can really see the structure of the Nanoparticle and a very gridlike structure when you look close.

  • @Diamonddavej
    @Diamonddavej 13 років тому +3

    Notice that colloidal gold is red?
    The ancient Egyptians were the first to make used gold nanopartices to color glass red (Ruby Glass) and in the 4th century, the Roman artisans used gold particles 6 nanometers wide to color the glass of Lycurgus Cup red.
    In 1908, Gustav Mie explained how colloidal Gold produce Ruby Glass, Mie Theory, localized surface plasmon oscillations on the surface of metal nanoparticles.

  • @yellowmetalcyborg
    @yellowmetalcyborg 13 років тому +3

    The awesome thing about looking at gold nanoparticles is that you don't have to plate them in gold in order to see them in an electron microscope.

  • @frederf3227
    @frederf3227 9 років тому +3

    I remember a professor once rattling off a calculation of "2 times pi, that's ten. Ten times fifteen that's 100, etc." All the operations were that sloppy and in the end the answer had something like 15 zeroes and the sloppy version was only 20% off the careful one.

  • @publiusdg
    @publiusdg 12 років тому +2

    I hope I'll be as excited as this guy in my future job. He makes his job look so fun.

  • @BobStinkfulla
    @BobStinkfulla 13 років тому

    @AVJRoutledge Electron Microscopes such as the one used to capture the pictures for this study are still being refined, but are approaching the limit of their resolution. This arises from the nature of the electron source used and from the inaccuracies in producing the electromagnetic lenses required to operate the instrument. Other types of microscopes, such as Atomic Force Microscopes of Scanning Tunnelling Microscopes are also capable of achieving atomic resolution and are being improved.

  • @habichturs4427
    @habichturs4427 12 років тому +2

    You see a detail of a metal mesh (usually Cu) purpose-made to hold thin foils or layers for TEM investigations. It is covered with a thin film of amorphopus carbon (a "holey carbon film"). The only thing you have to do is, get the gold particles nicely dispersed in their suspension (use an ultra-sound bath), and then let a droplet of that suspension dry on the TEM grid with the carbon film. Then put it into the TEM specimen holder, put that into the TEM, and you're ready to image .

  • @habichturs4427
    @habichturs4427 12 років тому +2

    One correction: In a typical TEM, the wavelength of the transmeitted electrons is not of the order of magnitude of the interatomic distances (or the distances of the lattice planes), but about two orders smaller. While phycisists are not always very exact, a ratio of just one order is usually described as much smaller, let alone two orders.

  • @TrueEmergence
    @TrueEmergence 13 років тому +2

    Oh my god. This channel is one of my favorites thusfar. Thank you so much for the posts.

  • @lasseankerfrederiksen2285
    @lasseankerfrederiksen2285 8 років тому +13

    I love to see this guy. he really gets so existed when he explains

  • @24938839
    @24938839 8 років тому +141

    I like the fact that he thinks americans know the size of Indiana

    • @fudgelame
      @fudgelame 7 років тому +1

      Ireland probs understandable than Indiana.

    • @VeggyZ
      @VeggyZ 7 років тому +1

      I think (hope) everyone watching this video knows at the very least that Indiana is roughly the same size as Ireland.
      Quite the mind-trip. But it's just an approximation.

    • @randellporter8747
      @randellporter8747 7 років тому

      Lactose69: Your a pompous idiot. I'm guessing a13 year old pompous idiot.

    • @-yeme-
      @-yeme- 7 років тому +1

      VeggyZ I had no idea how big Indiana was, or where it was until I looked just now. I knew it was a state and I was sure it wasnt one of the huge ones in the west but that was all. I wonder how many Americans would know how big the county of Devon, where I live, is, or be able to point it out on a map. A minority, I would imagine, and probably a small one.

    • @666wurm
      @666wurm 7 років тому +2

      Indian 94.321 km², Ireland 84.421 km² - that is 11.7% off! Ridiculous!

  • @brianwilson9501
    @brianwilson9501 6 років тому +4

    His energy is awesome. He would be a great teacher. Wish my teachers had half the energy he has.

  • @tonyhart97
    @tonyhart97 6 років тому +3

    I first watch this video when I was about 16 and was fascinated and now I'm doing my degree in nanotechnology and only a few weeks ago we made both Au and Ag NPS, it's cool to rewatch this video and see how far both I and the field have come in seven years

  • @habichturs4427
    @habichturs4427 12 років тому +1

    Yep, that estimate is about right. The TEM image is in simple terms a projected view of the crystal (not like your optical vision of some macroscopic object), so unless the columns of atoms are not aligned to the direction in which the electrons travel you can't see them separated. At 00:10 you see in one part of the crystal a stripe pattern which means that the electrons travelled parallel to planes of atoms (to be exact: parallel to planes far enough apart to be resolved by the microscope).

  • @IRuinEvrything
    @IRuinEvrything 12 років тому

    i don't know if there's a tech term for it, but I refer to it as proportional rounding. you have to round everything at its own scale. I imagine you can't really do it until you have a significant amount of intuition with the numeric behavior of a given quantity/quality. some things you round down, others you round up to bal out the behavior of the thing that was rounded down.

  • @luis5d6b
    @luis5d6b 12 років тому +1

    Honestly I would love to get a physic class with this guy or any of the guys from sixty simbols I really love to see when someone gives a class and really enjoys what he or she is teaching as much as I love learnig and it good with getting a lot of questions and intelectual debate about the subjects and this guys seems great, love this videos

  • @Derundurel
    @Derundurel 10 років тому +2

    I completely agree about people being uncomfortable with inexact quantities. Engineering is full of this sort of thing too - everything has a level of uncertainty attached. Sometimes an order of magnitude answer is sufficient.

  • @zantrua
    @zantrua 12 років тому +2

    I love how he holds up the paper for pretty much the whole interview. He's so excited haha

  • @w00td00t
    @w00td00t 13 років тому +1

    Awesome name, awesome taste in music, awesome profession. What isn't awesome about this guy?

  • @vevenaneathna
    @vevenaneathna 12 років тому +1

    maybe nano particles could be a viable medium for recording data due to the refraction of electrons.
    If only we were better at making them and had a way of easily observing them

  • @AVJRoutledge
    @AVJRoutledge 13 років тому +1

    I’m very addicted to all these. One question for anyone who knows the answer!!
    How much more powerful are these microscopes going to get?
    Have they reached a critical limit?
    Are there new ones coming out?
    Will they continue to be refined?
    Are we going to get even more detail?

  • @Waltham1892
    @Waltham1892 13 років тому +1

    If only every student could have a teacher like this...

  • @codykonior
    @codykonior 13 років тому +2

    I'd have liked some extra explanation on why nanoparticles are important. Perhaps a future episode? :-)

  • @Maverician
    @Maverician 9 років тому +9

    5:33 is amazing to keep clicking back to...
    Sorry Prof Moriarty.

  • @gulllars
    @gulllars 13 років тому

    @Robaaaayy it's like the quote from the theme song of flashdance, "Take your passion and make it happen".
    I was almost through the second year of chemistry in university when it hit me although i was skilled at it, i didn't have a passion for it, and my passion for computers, which had always been a hobby, had grown to the point i decided to do just that, make it happen. It feels like comming home without ever knowing you weren't there already, but at the same time deciding to do so is scary.

  • @ramonbril
    @ramonbril 13 років тому

    @calmo15
    It is not the diffraction that stores information, it is just that the difference between two lines of holes in the cd is about the wavelength of light. Though you can store information on nano particles if you hold the capability to write and read on that level.

  • @bwub1
    @bwub1 12 років тому +1

    Actually theyre already being used for some data sorage devices. Not in solution but attached to surfaces. There are loads of cool things you can do with nanoparticles. There are plenty of ways of making them too. Most of the chemistry is fairly simple so you can make them in a lab in an afternoon. Observing them is tricky becuse they're so small, but again there is about a dozen good techniques you can use to get an aproximation of their size and shape.

  • @michaelguckian5373
    @michaelguckian5373 8 років тому +4

    Have you / can you run some high speed camera imagining at the the nano scale. Maybe we can see movement of patricles image how quick things are moving at this scale.

  • @willwoodhouse
    @willwoodhouse 13 років тому

    @Agemrepus yeah it would but a lot of measuring equipment isn't actually accurate enough to measure that precisely, so its usually best to stick to relatively few D.P.s

  • @tomrich553
    @tomrich553 13 років тому +1

    i made these at my high school as well! it was incredibly fun, and because of it i plan to study nanotech at Leeds next year!

  • @criddell86
    @criddell86 13 років тому +2

    Possibilities of electrons being used to read/write to the surface of nano particles to store data in large volumes?

  • @Jumiconnard
    @Jumiconnard 13 років тому +1

    It looks like it has a 5-fold simmetry, just like quasicrystals :o

  • @1646Alex
    @1646Alex 12 років тому +2

    yeah, i know. but, i've really wanted to get into theoretical physics for like my whole life, but i've always sticked to more piratical carers, but this video has motivated me to become one.

  • @rushianokun
    @rushianokun 13 років тому +1

    I LOVE this guy, please feature him again!

  • @JustinRiedyk
    @JustinRiedyk 13 років тому +1

    It's mind blowing that the tiny particle is still 120,000 atoms.

  • @DoctorFastest
    @DoctorFastest 13 років тому +1

    @MrChemify My understanding is they use electrons because of the short wavelength. The problem with using DLS on something like this would be scattering off of multiple particles within a single wavelength, complicating the interpretation of the scattering significantly. I'm not an expert, but I'd be surprised if DLS worked on these scales. I know that it's useful for larger stuff, like proteins, polymers, etc.

  • @singlespies
    @singlespies 13 років тому +1

    I am most interested in the imaging process and enjoyed the explanation of the "lines" in the image of the nanoparticle. Was wondering if light cannot be used to image things that small and why...

  • @experthe9574
    @experthe9574 13 років тому

    This is such a coincidence, because just a few days ago I made gold nano particles for a class as well.

  • @RockMedved
    @RockMedved 13 років тому +1

    This is my favorite sixtysymbols guy.
    BTW I rather enjoyed the envelope part, since about 90% of my Maths calculations are all across my bills and envelopes too :D

  • @brandonX360
    @brandonX360 13 років тому +2

    Sixty Symbols is always good fun to watch!

  • @Dracanic
    @Dracanic 13 років тому +1

    I absolutely love this series. My goal is to get a physics degree and this channel is keeping that dream alive

  • @bigboam
    @bigboam 12 років тому +1

    My question is: does all of that rounding ultimately create minor errors? i.e. are we (ever so slightly) miscalculating the orbits of planets, etc., by rounding to three or four significant decimal figures?

  • @calmo15
    @calmo15 13 років тому

    if the nanoparticle diffracts electrons in the same way that CDs diffract light, would it be possible to store information on the and make like a nano hard drive?

  • @NordicLab
    @NordicLab 13 років тому

    which were obtained by these particles? Are there studies using dynamic light scattering?

  • @WildBillCox13
    @WildBillCox13 10 років тому +2

    Off topic, but is a neutron liquid (cf Neutron Star) stable enough to parse fractions of it and the parsed neutron components stay within the limits of a common surface tension? Or does any small amount of it (said neutron liquid sample) readily ablate into nothing? The reason I'm asking is that I've been wondering about element drip lines, pursuant to the possibility of artificially (is there any other way?) creating super nuclei in excess of those we've already achieved. Rather than using existing accretional methods of amalgamating heavier nuclei than those we find in nature, perhaps, could we, for sake of argument, begin with a matrix of neutronal moderator and thus overcome Coulomb resistance?

    • @Saki630
      @Saki630 10 років тому +1

      William Cox I have no idea what you are talking about. At the beginning you propose a thought experiment where you take a piece of a Neutron Star and try to stabilize the neutrons long enough for them to decay into elements? Then You want to have Neutronal Moderators to do what? I thought NM's were just atoms/molecules put in place to capture neutrons and slow them down as they pass through in nuclear reactors. Do you want to use NM's to stabilize this neutron star matter? Also why would you assume pieces of a Neutron Star are liquid?

    • @bbbilge
      @bbbilge 6 років тому +1

      Ultra heavy materials and welcome black hole?...

    • @robinswamidasan
      @robinswamidasan 5 років тому

      @@Saki630 Excellent response!

  • @e1doller
    @e1doller 13 років тому

    @isreasontaboo you can create these using a gold salt and trisodium citrate to reduce it. the lee and misel method is pretty well known.

  • @habichturs4427
    @habichturs4427 12 років тому +1

    Forget about your imagination of "size of an atom". All what matters here is the electric potential which deflects the electrons, in other words, affects the phase of the wave of the fast transmitted electrons. Gold atoms have a high Z (large charge in the nucleus) meaning they have a high scattering cross-section. You could detect an individual Au atom with a good TEM (better with a STEM). However, it is energetically so favourable for the atoms to stick together that none would separate).

    • @bbbilge
      @bbbilge 6 років тому

      Doğada ALTIN zaten en çok sularımızda iyonize halde bulunmakta tüm canlıların metobolizmalarına dahil olmaktadır. Paradan farklı olarak altın iyonize olarak yenilebilir ve etkileri gerçeküstü gerçeklik ötesidir. DMT ruh ya da tanrı molekülü sentezlenmesinde metabolik olarak işlevseldir.
      İki Türk bilim insanı suda iyonize halde bulunan altın atomlarını virüsleri genetik olarak yeniden modifiye ederek toplamayı başarmışlardır. Bu süreç başta akıllı yaşam türleri olmak üzere dünya üzerindeki canlı yaşam türleri ve beyin sinir aktivasyonları için uzun vadede geri dönülemez etkilere neden olabilir.

  • @JuanLeTwnz
    @JuanLeTwnz 13 років тому

    I really didn't expect him to take Rated R out of the cupboard.
    Makes me want to give this vid 1 quintillion thumbs up :)

  • @arothn89
    @arothn89 12 років тому +1

    queens of the stone age, this guy just keeps getting cooler!!

  • @sniped101
    @sniped101 12 років тому +1

    If I had one of these guys as a teacher when I was in middle or even highschool, I'd probably be a physics major..

  • @NordicLab
    @NordicLab 13 років тому

    @DoctorFastest I use a laser at 720 nm wavelength for DLS. According to his passport instrument measures the size of 0.8 nm. But if he could see the separate particles, I do not know. At least I got it a size of 3-5 nm with mixed peaks.

  • @frysebox1
    @frysebox1 12 років тому

    @PappaKnowsBest
    I'm pretty sure if I just solved for the symbol representing the value and unit of what you're looking for in a question through algebra, and didn't bother to put in any of the values given for any of the questions, I'd still get an okay grade on my physics exam.
    We've always been told in maths and physics that how you get there is the important part.
    Also if you answer with a number but don't account for valid decimals but just write what your calculator says, you lose points.

  • @vanessacherche6393
    @vanessacherche6393 10 років тому +10

    Excellent choice for random cd on bookshelf!

  • @evilferris
    @evilferris 13 років тому +6

    @ThermalHD
    $52 per g; current gold price in grams
    197 g in a mole
    6.023×10^23 atoms in a mole
    125,000 atoms/particle or 1.25×10^5 atoms
    (1.25×10^5) / (6.023×10^23)= 2.075×10^-19 mole
    (2.075 × 10^(-19) × 197g = 4.088 × 10^(-17)g
    4.088 × 10^(-17) × $52 = $2.13 × 10^(-15) or
    $.00000000000000213
    Somebody check my math?

    • @zeryphex
      @zeryphex 6 років тому

      @evilferris
      I'm sure your math is ok ... but there could be billions of dollars made from collecting gold particles in all the world's oceans ... and plenty of gold from recovery in electronics waste.

    • @teyton90
      @teyton90 6 років тому

      i'm sure it's ok, since you had 7 years to figure it out

  • @FalcoGer
    @FalcoGer 12 років тому

    the wavelength of the electrons that were used to make that image...
    i wasn't even suprised to hear that anymore, i even guessed that before you said it

  • @richardfrieman
    @richardfrieman 7 років тому +2

    I know I'm like 7 years late, but the statement about crystal faces was flawed. Although it's true that Diamonds have crystalline structure, we never see it grow out. Raw diamonds are rough because they grow within a matrix of ultrabasic magma that formed within Earth's mantle. They then get eroded out at the surface where they are subsequently found often on beaches of oceans and rivers. The facets that we see on diamonds are cut and polished by humans. Quartz would have been a better analog; when quartz is allowed to grow in a void, it forms beautiful obelisk shapes with naturally occurring crystal faces like those on the gold nanoparticle.

  • @jerommeke69
    @jerommeke69 13 років тому

    @singlespies
    nope, light cannot be used.
    Look up "angular resolution" on Wikipedia to learn why!

  • @cristianfcao
    @cristianfcao 13 років тому +1

    Some weeks ago I've learned how many atoms are in a grain of salt.
    Are you ready?
    About 1.2 *10 ^ 18, or: 1,200,000,000,000,000,000 atoms!!
    That fact alone multiplied my admiration for particle physicists by at least a billion. :-)
    I mean how is it possible to study something so unimaginable small? That there are protons, neutrons and electrons, which are so much smaller than the atom itself, and then quarks within the protons and neutrons that are smaller still!!

  • @adeel256
    @adeel256 11 років тому +1

    love the little diversion. that's what makes it human. beautiful!

  • @FrostPegasus
    @FrostPegasus 13 років тому

    How come the electrons from an electron microscope don't react with the atoms you're trying to view?

  • @iowanthomas
    @iowanthomas 13 років тому +3

    This man is truely inspirational, I would pay a very large sum of money to spend time learning with him.

  • @krazedgunner
    @krazedgunner 13 років тому +1

    I love videos like this, im getting interesting just learning about it. can I ask you about that electron microscope? is it over $15 grand :)

  • @Agemrepus
    @Agemrepus 13 років тому +1

    I just always wonder this (yes, I AM a first year haha), but if you were to take everything to the 19th decimal (or more), wouldn't that make all of your calculations even more accurate? And wouldn't that in tern aid in better conclusions?

  • @drakan
    @drakan 12 років тому +1

    depends upon where within the equation you're rounding, to be honest. You round something at the beginning, it's going to progressively get more and more inaccurate as you scale the value upward

  • @beeble2003
    @beeble2003 12 років тому

    I was talking about average speed, not top speed. My point was about errors in measurement: it doesn't make sense to quote the average speed to five significant figures when you've only measured things to three.

  • @jean-pierrevandermerwe7604
    @jean-pierrevandermerwe7604 11 років тому

    Could gold or other nano crystals be used to store data on a nano scale like a CD would???

  • @borandiUK
    @borandiUK 10 років тому +5

    Shame he didn't start talking about the quantum dot effect, and that different sizes of gold nanoparticles produce different colours.

  • @Confuseddave
    @Confuseddave 7 років тому +3

    I thought the SI unit for large size comparisons was Wales.

  • @RM_RM_RM
    @RM_RM_RM Рік тому

    Very beautiful 5-fold twin of gold

  • @Drag0nfoxx
    @Drag0nfoxx 13 років тому

    @Ormaaj as far as I know single atoms can only be seen directly via a scanning tunneling microscope (something like that, i'm not completely sure about the name).

  • @4405jack
    @4405jack 13 років тому

    I love this guy haha! Is there anyway to find out his name, so I could buy a book if he has written one?

  • @BobStinkfulla
    @BobStinkfulla 13 років тому

    @managarm1349 Yes, a Transmission Electron Microscope (TEM).

  • @1vrsc
    @1vrsc 11 років тому +1

    awesome stuff! American Idol zombies don't know what they are missing...should be watching things such as this. This is where real talent is...science

  • @subach
    @subach 13 років тому

    I do the same thing when I need to do a side calculation I just grab the nearest thing I can write on. No envelopes, but I've written equations on a few Chinese food menus.

  • @bitlhninja
    @bitlhninja 13 років тому

    what is the white space between nanoparticle and the big white circle

  • @isreasontaboo
    @isreasontaboo 13 років тому

    How are these created? Using some sort of chemical vapour deposition techniques?

  • @calmo15
    @calmo15 13 років тому

    @Brillyr thats what im saying, could you use the diffraction patterns to read the information?

  • @aeroscope
    @aeroscope 13 років тому

    I made gold nanoparticles at home, how do i preserve it? it keeps precipitating out

  • @Musicguy208
    @Musicguy208 13 років тому +1

    Always awesome! I love these videos!

  • @ItsNickFox
    @ItsNickFox 11 років тому

    What you typed would only tell you how many atoms wide the nanoparticle is. Instead, you need to find the VOLUME of the particle and the atom and divide the former by the latter. Assume both are perfect spheres for simplicity's sake and you'll get the proper answer.

  • @dezerterone
    @dezerterone 9 років тому +2

    'Restricted' - good choice! :)

  • @ifsey
    @ifsey 13 років тому

    4:12 Some nice product placement there! Malteasers- Food for thought!

  • @BamaFanEdge
    @BamaFanEdge 11 років тому

    Just to clarify, does nanoparticle just mean really small bit of gold? Is it like a flake of gold?

  • @rmenchoachupicachu
    @rmenchoachupicachu 11 років тому

    from what I understand, these nanoparticles are clumps of gold atoms that are mixed with another element to form these particles which are in the solution. The structure is confuses me though.

  • @pro4skill
    @pro4skill 12 років тому

    The uncertainty principle says that we can't know a wave-like particle's velocity if we know its position, and vice versa. This principle does not apply to calculating the volume/diameter of something.
    Seeing atoms also does not deal with the uncertainty principle; they are not wave-like, though they consist of wave-like particles. Not seeing the individual atoms is due to the fact that they are so incredibly small, and the zoom of that particular picture was too big to capture individual atoms.

  • @joanpuig0
    @joanpuig0 13 років тому

    @afhdfh He says "facets", which is the word for a crystal's (or any geometric object) flat face

  • @Americanbadashh
    @Americanbadashh 13 років тому

    @JonnMcNally
    Agreed

  • @RobertSeattle
    @RobertSeattle 13 років тому

    Where can you get those crystal models he shows?

  • @PacRimJim
    @PacRimJim 10 років тому

    It's not necessary to compute exactly, but it is essential to know how to compute exactly.

  • @Goodwithwood69
    @Goodwithwood69 9 років тому +4

    QOTSA best album by far!

  • @beeble2003
    @beeble2003 12 років тому

    There are errors but they're from imprecise measurement, not rounding. For example, Usain Bolt ran 100m in 9.58s. It doesn't make sense to give his speed as 37.578 km/h because the real distance might have been 99.98m (rounded to 100m) and the real time 9.576s (rounded to 9.58s), which is 37.586 km/h. For this reason, you only quote calculated values to a degree of precision equivalent to the precision of the original measurements. (In this case, the time is only accurate to one part in 1000.)

  • @djangogeek
    @djangogeek 8 років тому +1

    +Philip Moriarty
    So are the diffraction patterns from the electrons scattering constructive interference?

    • @robinswamidasan
      @robinswamidasan 5 років тому

      Alternating constructive and destructive interference.

  • @m.c.4674
    @m.c.4674 3 роки тому

    Why can't I see the atoms of the ground the crystal is on .
    I would like a detailed explanation how your instruments work

  • @omegahunter9
    @omegahunter9 13 років тому

    Now we need to make a nano particle CD out of some material. :)

  • @BoredErica
    @BoredErica 10 років тому +1

    If an object is smaller than a wavelength of visible light, what color will it look like to our eyes? Or is that irrelevant?

    • @louistournas120
      @louistournas120 9 років тому +1

      Virtualgod2009 "invisible. What color is ultraviolet and x-rays?"
      ==People who have had eye operation, where the lens get replaced describe it as blue with some whitish hue. This is because the artificial lens lets UV light through. UV mostly excites the same receptors as blue light plus some of red and green.
      X-rays would probably knock off electrons all over the place and cause fluorescence and appear white.

    • @redo348
      @redo348 9 років тому

      Eric Lin It depends what it is and how you look at it.
      Gold nanoparticles scatter green light. And you really can see individual ones with a standard optical microscope (just not their shape).

  • @rkaith
    @rkaith 11 років тому

    Can u make it even smaller maybe single atoms??

  • @BYMYSYD
    @BYMYSYD 13 років тому

    i do the same thing. If all of the sudden i need to calculate something. i do it on the back of an envelope or index card.

  • @guerra_dos_bichos
    @guerra_dos_bichos 9 років тому

    What is the value o pi? about 4...