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      "body": "![](https://steemitimages.com/DQmQmJayjPkA1HafHWVD4WErzJGBpffbhdJqt7uM49SCz46/image.png)\n[Source](https://pixabay.com/en/heart-card-pastels-figure-762564/)\n\nValentine's Day is a time for happiness and a time for being with loved ones. Or maybe not. From New Year's Day to Valentine's Day, people think about breaking up more than any other time of the year [[1]](http://abcnews.go.com/US/story?id=2863607&page=1). So, although it's Valentine’s Day, there may be a little bit of sadness brewing. However, fear not! The Valentines that we will be making are useful to both those with and without love in their life. If you have a special someone in your life, then you will be able to give them a PERFECT Valentine made with MATH. If you are without a special someone, come with me. We will numb our brains on something better than alcohol. You know I’m talking about Calculus. And who knows? Maybe this will help you hook up with a math minded individual.\n\nAlright, so what is the most important aspect of the Valentine? Is it the message? Is it the card itself? Is it the chocolate and/or flowers that goes with it? Absolutely not! It is the heart drawing. Every Valentine needs a heart and if you can draw the PERFECT heart then you will have the PERFECT Valentine.\n\nHow can we draw the perfect heart? With online graphing tools. Duh. I recommend using [Desmos](https://www.desmos.com/calculator/ksjcpazwa9).\n\nIf you have taken any algebra courses, you may be wondering how graphing a heart is even possible. After all, if you were to put a heart on graph paper you would notice that it does not pass the vertical line test. However, failing the vertical line test ONLY proves that the tested equation does not have y as a function of x. This means we can graph just about anything using the correct perimeters. For example, y^2 = x does not pass the vertical line test, but it is easily graphed by plugging in points.\n![Ex. A.PNG](https://steemitimages.com/DQmdRQJnBZxGzEvhSzajn6iHBifuhd1kCHVxyyMPMJ5nMXD/Ex.%20A.PNG)\n\n## Alright, let us begin!\n\nEquation 1:\n![Eq.1.PNG](https://steemitimages.com/DQmaDyu1d2CbTU4kJtRbk9QWfHmakXbp1NRgz6XkwtuyWVG/Eq.1.PNG)\n![Ex. 1.PNG](https://steemitimages.com/DQmcxsEffyCgfC57eVYi7VCgoAY8fDnhrk85VcrfdCRDsYc/Ex.%201.PNG)\n\nAlright, let’s start this off with something relatively easy. This equation is a good start. At its core, it is just a variation of an equation for a circle (x^2+y^2=1). This equation is also in simple y/x (Cartesian) coordinates so there isn’t too much going on. However, this graph proves less is more. The easy format makes it easy to plot, and you could graph it at home right now if you really wanted to. I would rate this equation as 8 hearts out of 10.\n\nEquation 2:\n![Eq.2.PNG](https://steemitimages.com/DQmR74qoi1TtGpKuQKGS7YrgsCpzvdWAKY65AW7cWdgMV7T/Eq.2.PNG)\n![Ex. 2.PNG](https://steemitimages.com/DQmUTxxV4GcUKwANJuhHd8ZmteFahvDjnswJ2skTKNbrV9s/Ex.%202.PNG)\n\nThis equation is for a cardioid named after, you guessed it, its heart-like shape. The cardioid appears in calculus quite often and any mathematician is sure to recognize it. However, the cardioid is in polar coordinates making it more difficult to graph. Polar coordinates are in terms of “theta” and “r.” If you are unfamiliar with polar coordinates, you may be wondering what “r” and “theta” represent. r^2 = x^2 + y^2 and theta is the angle of a right triangle if x and y were sides.\n![](https://steemitimages.com/DQmVD9Zj1dwS4RsbvjDzGHfyvsacEN9PQV9po4XyDKorZqi/image.png)\n[Source](https://en.wikipedia.org/wiki/Polar_coordinate_system#/media/File:Polar_to_cartesian.svg)\n I know it’s confusing, but that’s why its calculus. (Is your mind going numb yet?) Unfortunately, the cardioid is a little ugly compared to its competitor. It could barely pass as a heart. With all this in mind, I give the cardioid 5 hearts out of 10.\n\nEquation 3: \n![Eq.3.PNG](https://steemitimages.com/DQmcBAzt41jicwvEdVWATvAm25d6rkzGTwTt8xd6U341cYH/Eq.3.PNG)\nx=16(sin(t))^3, y=13cos(t)-5cos(2t)-2cos(3t)-cos(4t)\n![Ex. 3.PNG](https://steemitimages.com/DQmREA5NnNysGEALoZHxEDcJFii7deVNKmsuYevPMpcpWXE/Ex.%203.PNG)\n\nSo, this last one is a little bit more complex for sure. You may have noticed that this equation is in terms of “t.” That is because it is in parametric coordinates. Graphing this is probably easier than what you may be thinking. Pick any value for “t” and plug it in. Solve for the y/x values. Then, use the solved values to graph. \nThe equation just looks worse than it actually is. In reality, the equation given is really just another manipulation of a circle. The parametric equation for a circle is sin(t) = x, cos(t) = y. This is obviously a lot messier, but look at that perfect heart. It is voluptuous and curvy. Indeed, this heart is something special. I give it 10 hearts out of 10 and I think it is the perfect heart for which we are all looking.\n\t\nNow that we have several candidates, its time to make a Valentine. Get out any kind of paper (preferable graphing paper) and write your favorite equation and graph it. Your done! You just created the perfect Valentine. Anything else, like a meaningful message, would just get in the way. Trust in the heart and let it do its magic. I guarantee that you will become instantly more attractive and you will feel much more accomplished!\n\nObviously, I have not listed every equation that yields a heart when graphed. There might be some easier ones and I am sure that there are harder ones. Also, by using the z-axis it is possible to make a 3-Dimensional heart… but let’s not do that today (maybe next year). Also, all of the graphs are pretty fun to play around with. Sometimes little changes can dramatically change the shape. There are some interesting links below. Thanks for reading and Happy Valentine’s Day.\n___________________________________________________________________________________________________\n*I made most of the photos with Desmos, an awesome online graphing tool. Also, any comments or feedback is always appreciated.*\n___________________________________________________________________________________________________\nSources:\nhttp://www.mathematische-basteleien.de/heart.htm\nhttp://mathworld.wolfram.com/HeartCurve.html\nhttps://www.desmos.com/calculator/ksjcpazwa9\nhttp://abcnews.go.com/US/story?id=2863607&page=1",
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      "body": "# **The Miracle Material**\n\nAndre Geim, a physicist, was a brilliant researcher working for the University of Manchester. Besides working on just one research project, Geim took on many temporary projects. He called them “Friday night experiments.” Our story begins in 2002, when Geim assigned a graduate student one of these “Friday night experiments” to help him get acquainted with the lab. The experiment was simple. Try to get graphite as thin as possible. Geim also worked on the experiment with his colleagues, and in a sudden moment of brilliance, a colleague brought Geim a simple piece of scotch tape that was recently taken from a graphite surface [[1]](http://www.mypearsonstore.com/bookstore/chemistry-structure-and-properties-0134293932). By 2004, two men, Andre Geim and his closest colleague, Konstantin Novoselov had isolated the flakes on the scotch tape and studied them. They had discovered something truly amazing. They had discovered a material that was only one atom thick (Yes, the thinnest material). This material was also as strong as it was thin. Upon further examination, this material was 200 times the strength of steel and only one-sixteenth as dense. It could bend, stretch, flip, or be folded[[2]](http://www.graphene.manchester.ac.uk/explore/what-can-graphene-do/). Yes, I am talking about **graphene**.\n\n## **What is graphene?**\n\n###### **Structure**\nGraphene’s exceptionality is best understood through its crystalline lattices. A crystalline lattice is the natural way the atoms of a crystalline solid aggregate to minimize their energy[[1]](http://www.mypearsonstore.com/bookstore/chemistry-structure-and-properties-0134293932). You can think of a lattice as a crystal structure. Different lattice structures change the properties of the materials they make up. A few examples of materials with crystalline lattices are quartz, ice, salt, and diamonds. Here is a picture of graphene’s lattice.\n\n![graphene.png](https://steemitimages.com/DQmd7xg1wP5SsLuRqtXUTkQZQLKGMeQC1cBfbLTf9g6mzHR/graphene.png)\n[Image Source](https://en.wikipedia.org/wiki/Graphene#/media/File:Graphen.jpg)\n\nGraphene has a simple 2-dimensional hexagonal lattice structure. Usually, lattice structures are pretty difficult to understand because most are 3-dimensional, but graphene’s is 2-dimensional. Graphene’s 2-dimensional structure is one of the two reasons why graphene is so strong. All the bonds in graphene are on a singular plane. This means that if you were to somehow pull on a graphene nanoribbon, all (or most) the bonds would be working against you[[3]](https://www.chemguide.co.uk/atoms/structures/giantcov.html). For reference, steel is typically a body centered lattice and diamonds have a special kind of lattice structure called diamond cubic. Here are some pictures. \nhttps://upload.wikimedia.org/wikipedia/commons/2/22/Diamond_Cubic-F_lattice_animation.gif\n[Diamond Cubic](https://en.wikipedia.org/wiki/Diamond_cubic#/media/File:Diamond_Cubic-F_lattice_animation.gif)\n\n![graphene.png](https://steemitimages.com/DQmYyfYJEsRwDdMwrJVnbrQEmKK2J2tBVKHAs5poWdFCDgo/graphene.png)\n[Body centered](https://en.wikipedia.org/wiki/Cubic_crystal_system#/media/File:CsCl_crystal.png)\n\nSteel has a greater packing efficiency than graphene (as seen above). An important thing to note is compactness doesn’t necessarily mean strength. However, compactness is directly correlated with density. This is why the open lattice of graphene is one-sixteenth the density of steel.\n\n###### **Bonds**\n\nIn case you haven’t realized it yet, graphene is completely made up of carbon. These carbon atoms are held together in their lattice by powerful covalent bonds, the same bonds used in diamonds. Because of these powerful bonds, graphene has a high melting point[[3]](https://www.chemguide.co.uk/atoms/structures/giantcov.html). A key difference between the carbon atoms of diamond and the carbon atoms of graphene is their hybridization. Graphene has an sp^2 hybridization while diamond has an sp^3 hybridization. For our purposes, hybridization determines how many bonds carbon will have. Sp^2 means carbon will bond with 3 atoms and sp^3 means carbon will bond with four [[4]](http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch10/carbon.php). Carbon typically likes to have four bonds because it has four valence electrons. Graphene’s carbon atoms only use three out of their four valence electrons on bonds. What, you may be wondering, is this one, lone electron doing? Well, this electron is a free-floating electron and it grants graphene the ability to conduct electricity. This is a very important property. Sometimes, the free-floating electrons will bond with another, making the bonds within graphene even stronger. [[3]](https://www.chemguide.co.uk/atoms/structures/giantcov.html)(Because even electrons want friends too…)\nhttps://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Covalent.svg/334px-Covalent.svg.png\n[Covalent Bonds in Methane](https://en.wikipedia.org/wiki/Covalent_bond#/media/File:Covalent.svg)\n\nWell, if graphene is so strong, why does graphite seem so weak? After all, graphite is just stacked graphene. Well, graphene doesn’t bond well when stacked. Instead of strong covalent bonds, graphene uses a weak and pitiful intermolecular force known as London dispersion forces [[5]](https://en.wikipedia.org/wiki/Graphite). Just about every molecule experiences these forces, and they are the reason why pencils can write. A good analogy is think of graphite as a stack of cards. The individual card is strong, but this does not translate to a durable stack of cards. Instead, they will slide off one another with just a gentle push.\n![Cardz.jpg](https://steemitimages.com/DQmbJZwW5rwAiPhBCmpQKUVC1N9CLEsxqoV5YsedoeW79yU/Cardz.jpg)\n[Image Source](https://www.pexels.com/photo/playing-game-card-58562/)\n\n###### **Is graphene useful?**\n\nHopefully by now, you have a good idea of why graphene can be so strong but also so light and flexible. But, like my high school English teacher would say about my papers, “so what?” (I got a C in English that year). Is graphene useful? The answer is obviously yes. Graphene has many qualities which makes it useful in a broad range of subjects. Remember when I told you it was a good conductor. Graphene has a strong future in electronics. Studies show that it could be used for one of the most energy efficient transistors ever [[6]](http://www.thegraphenecouncil.org/?page=ElectronicsJAN15). Others foresee graphene being used in flexible/foldable touchscreens [[2]](http://www.graphene.manchester.ac.uk/explore/the-applications/electronics/). It doesn’t stop at electronics. Because of graphene’s high melting point, there is talk of using graphene in the automotive industry which could save as much as 30% to 50% in automotive structural weight while also adding more safety to the operator.[[7]](http://articles.sae.org/13441/). In biomedical engineering, there is talk of using graphene for tissue regeneration[[8]](http://pubs.rsc.org/en/content/articlelanding/2013/tb/c3tb20405g#!divAbstract). Honestly, the uses for graphene are limited only by our imagination. \n\nAre we already using it? What are we using graphene for right now? Well, graphene is being used in censors. Think about it. Every atom of graphene is exposed to its environment [[3]](htp://www.graphene.manchester.ac.uk/explore/the-applications/sensors/0). When applied, graphene can make for incredibly accurate censors that can distinguish materials down to the molecule. \nIf you want to get a glimpse of the future, googling “potential uses for graphene,” is probably a good way to do it. Graphene is still a relatively new discovery, but I would classify it as a major discovery. I am excited to see what becomes of graphene and I hope you are too.\n\n\n\n___________________________________________________________________________________________________\n\n*(Hey! Thank you for reading! I had a lot of fun researching and writing this post. If you have any feedback for me, you can comment below. That is always helpful and appreciated. My next post will be sometime this weekend. Thanks again for reading and I hope to see you again soon!\n-ulearn)*\n\n___________________________________________________________________________________________________\nSources\nhttp://www.mypearsonstore.com/bookstore/chemistry-structure-and-properties-0134293932\nhttp://www.graphene.manchester.ac.uk/explore/the-applications/electronics/\nhttps://www.chemguide.co.uk/atoms/structures/giantcov.html\nhttp://chemed.chem.purdue.edu/genchem/topicreview/bp/ch10/carbon.php\nhttps://en.wikipedia.org/wiki/Graphite\nhttp://www.thegraphenecouncil.org/?page=ElectronicsJAN15\nhttp://articles.sae.org/13441/\nhttp://pubs.rsc.org/en/content/articlelanding/2013/tb/c3tb20405g#!divAbstract",
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      "body": "They must! The bibliography is very important. And with good references! But we still need to produce a lot and get to know a lot to evolve in these areas. And that's just a hit and miss. They should and are not always, well-supervised so as not to be unethical and to endanger human lives.",
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      "body": "Carbon plays a fundamental role in all life and everybody uses it everyday. Carbon is a tramp!",
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      "body": "I completely agree. Many news networks make their money through advertisements. Scary headlines are just better at bringing in a larger audience. Many studies, not just one, are needed to determine the dangers involved in anything. I think any article making such a large claim should cite multiple studies to back up their point.",
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      "body": "Pretty much anything in moderation is fine. Good article!",
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      "body": "Now I feel like eating a carrot. Good article!",
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