Subtitles section Play video Print subtitles Oh Hi, I didn't see you come in Do you feel this... connection that we have? I've been feeling it all day I know Are you thinking what I'm thinking? No no, you say it first You... okay, I'll say it Six thousand six hundred and six point forty-eight divided by two Oh There are a lot of people watching this right now? I guess we should explain what we just did six thousand six hundred and six point four eight is the approximate value of this mathematical expression A hundred and twenty eight times the square root of the base of the natural logarithm times nine hundred and eighty Divided by two is important because if you take this expression and divide it in half you get "I love you" But love isn't always easy sometimes there will be arguments, differences but love can endure any... inequality? Specifically this inequality discovered by Albert Einstein but not really I'm just making all of this up Anyway, this inequality tells us that 9x plus 7i You have to use some imagination with love is less than three times (3x plus 7u) Now, let's simplify this inequality and see what we get Well let's distribute the three and so we'll wind up with 9x plus 21u and that is less than 9x plus 7i Now what we can do is subtract 9x from both sides and that will give us 7i is less than 21u We can divide both sides by 7 to find the true meaning of my entire life Divided by 7 we get I I heart I heart you But why "say" how you feel when you can show..."how" you feel? What I mean by that is Neurotransmitters Serotonin and dopamine necklaces are a great way of showing what's happening in your brain when you see that special someone My favorite romantic gift comes from MathsGear.co.uk I actually got a pair of these for me and my wife I think she's lost her half But it doesn't matter because it's the thought that counts These are amicable numbers What are amicable numbers? Well there are two numbers that share a special bond Take the number 220 What positive numbers evenly divide into it? Well... 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and a 110 If you sum all of those up, you get 284 But what positive numbers divide evenly into 284? Well in that case we've got 1, 2, 4, 71 and 142 ...whose total sum is 220 Beautiful right? That relationship touches my heart in all kinds of special ways But let's talk about heart shapes because heart shapes can be mathematically generated my favorite way of course is the Cardioid The path traced by a point on the circumference of a circle rolling around the outside of a circle whose diameter is equal But... But(t)... is what it looks like a butt But also Cardioids don't have points If you want a point, there are equations for those kinds of hearts There's even an equation for a great heart surface but I know what you're thinking Michael... I watch Rick and Morty, okay I don't want a symbol for a heart I know that anatomically hearts look different Well, you're in luck Because anatomically correct diagrams of hearts can be found on cards, on posters, on mugs... this pendant is just wonderful But look at this vase ah it's just so heart-like it's kind of macabre but hold on a second If you really really want a romantic gift that is extremely pedantic why get an anatomically correct diagram of a heart when you could get a literal heart PrestonsMasterButchers.co.nz will sell you literal animal hearts And if that doesn't say "I love you" then you've got a lot of other better options at the end of the day, the most romantic gift is the gift you made yourself Let's make some mathematical romance we're gonna begin with a strip a strip of paper I can take a strip of paper and turn it into a hoop shape a cylinder with no top or bottom when I have some tape now if I tape this hoop together and cut it in half what will I get? Well I will get two halves I can prove it to you in case you don't believe me I'll make a snip right there and I'm gonna start cutting around the middle of the strip all the way around and when I meet back up lo and behold I've got two hoops Nothing too surprising here You could turn this into some kind of mathematical you know, love bracelet or maybe it's like a ring if your partner has extremely fat fingers But we're not here to talk about simple hoops We're here to talk about the Mobius strip A Mobius strip is made just like a hoop except before you connect both of the ends of the strip you give one end a 180 degree turn we'll call that a flip so watch what I do as I turn this 180 degrees Now I will tape these two sides together make sure I get plenty of tape so that nothing comes loose and now I have myself a mobius strip I'm sure many of you have played with these before have you ever cut one in half? the way we cut the hoop in half Let's see what happens when I try if I cut it right there so that there's a little hole to pull my scissors through and I start cutting right down the middle I should of course wind up with two thinner Mobius strips It's not cut in half I've just made a thinner wider loop that actually has more twists There are four twists in this now Numberphile has a fantastic series of videos about why this happens You might be wondering where's the romance well here's what we're gonna do We're going to take two strips of paper and we're gonna make two mobius strips of opposite chirality Chirality has to do with which direction we turn the strip in before we tape it so for this first one I'm going to turn it what is clockwise to me Perfect and I will tape this Always be sure to use lots of tape because if it comes loose while you're cutting Well, you're gonna be single for the rest of your life now with my other strip, I'm going to turn counterclockwise from my perspective and tape it what I'm gonna be left with is two mobius strips that have opposite handedness, or chirality They will be mirror reflections of each other See that? Mirror reflections And now I'm going to tape them together You can tape them however you want But again, the rule always stands to use plenty of tape so that after the cutting the pieces stay together all right, so there's.. I'm gonna put more tape on I'm just really nervous about this falling apart