Mathematics of Change Project
Essential Research Question: How can we connect concepts of geometry in crystal formation and the process in making rock candy?
In our first brainstorm, to get inspiration, we created a list of topics that we are interested in and decided that it would be really fun and interesting to do our project on something related to culinary arts. We were aware that there are known sciences, but we were unfamiliar to the mathematics associated with cooking. Our group agreed on making something unique and taking an approach that would grab someone’s attention and so the project began with us researching how math can connect to candy. We stuck with this topic because it is different and appealing to a wide audience. From there, we decided to make something that is kid friendly and interactive, something that would keep spectators entertained.
For our project, we created a two minute video that explains the seven different monoclinic crystal systems. During our first set of research on how rock candy is formed, we came across the mathematical formations of crystals and the relationship it shares with chemistry. We learned about the chemical process in making rock candy, and how evaporation and fractals in crystallization play a key part in the process. From this, we discovered a source called, The Forbidden Crystal Symmetry that describes how geometry is connected to the formation of crystals as well. We explored the geometry formulas behind why the remaining sugar content form the particular crystal like shapes rather than any other shape, specifically fractals in crystallization.
We learned that there are many different stages of solid sugar crystals to a sugar liquid that is used to make hard candy. The stages have varying temperatures and state description. One source that we found very useful is a filmed lecture from www.richannel.org on the structure and geometry of crystals. We learned that there is energy released when they are heated and different sugars react in different ways. From www.curiouscook.com we learned that heat energy makes atoms move faster. As sugar heats up in the pan, its molecules get more and more jittery, to the point that their jitters overcome the attractive forces and they can jump from one set of neighbors to another, meaning it liquefies. We figured out that The change in solubility with change in temperature can be used to create solutions with more solute dissolved than is predicted by the solubility of the substance.
The most helpful website for our research was http://projectsharetexas.org/resource/types-solutions-saturated-supersaturated-or-unsaturate-ontrack-chemistry-module-5-lesson-3 because it defined some important terminology to better understand our topic. There are three solutions that can be given solute and solvent which are unsaturated, saturated and supersaturated. The unsaturated solution does not reach the limit of solubility. The saturated solution has “reached its limit of solubility for a solute at a given temperature”. The supersaturated solution holds “more dissolved solute than it normally would at a given temperature”. This means, by boiling the water and dissolving the sugar, it allows the rock candy solution to cool. If more crystals of the solute are added, they act as seed crystals in nucleation sites for crystal formation. According to Wikipedia, seed crystals are a “small piece of single crystal / polycrystal material from which a large crystal of the same material typically is to be grown. The large crystal can be grown by dipping the seed into a supersaturated solution, into molten material that is then cooled, or by growth on the seed face by passing vapor of the material to be grown over it.” With this information, we further tried to understand the monoclinic crystal formations and the formulas that are involved.
We also learned about crystal lattices, and how when white sugar is heated it breaks off (not breaking down) and separates from it’s crystal bond, forming a liquid. When this liquid cools off, the distance between the individual sugar molecules comes in close again, in the case of making rock candy they hug on the lollipop stick, and they begin to reform they're crystal shape. It is the way they come together, in a unique bond that gives them the distinctive crystal shape. As the candy cools, its contents condense and harden, and the separation goes away as the molecules cling together.
In our project gave a “crash course” of how the mathematics applied in crystal formations. We have found information on the different formations sugars make under certain amounts of heat. Then combining through the cooling process and therefore forming crystals. We also found some resources that explain how crystals take on the geometrical shapes that they do. As a group annotated the formulas to figure out the meaning behind them, then simplified them so they are teachable to a broader audience. Overall, we want our audience to understand the basics of geometry in crystal formation and how it connects to the process in making rock candy. Our script says, “The first thing you will need to know about crystal formation is that there are seven different crystal systems. This includes the triclinic, monoclinic, orthorhombic, tetragonal, trigonal, cubic and hexagonal systems. For this video, we will primarily cover the monoclinic crystal system. The monoclinic system has three unequal axes. The vertical axes are inclined toward each other which creates an oblique angle. The horizontal axis is perpendicular to the other two axes to form a rectangular prism with a parallelogram as its base. These angles are all arranged 90° to each other and are made up of six faces. The monoclinic crystal system is also one of the seven lattice point groups and is described by three vectors. The crystal lattice can be thought of as an array of 'small boxes' infinitely repeating in all three directions. The symmetry properties of the crystal are embodied in its space group. A crystal's structure and symmetry play a role in determining many of its physical properties. Sucrose, for example, starts out with a crystalline structure, specifically in the monoclinic space group. When making rock candy, the sucrose is heated with water to make a supersaturated solution. As it is heated, the crystal lattice structure of the sucrose is disrupted or broken. Once left to cool, the sugar in the solution then begins to crystallize - changing from a liquid to a solid. As the sugar crystals begin to grow; the atoms that make up the sugar align themselves and bond with atoms of the sugar crystal that are growing. Energy is released and the cycle of bonding and growing continues in all directions to once again form a lattice structure but of larger, more pure crystals than the original sucrose. In nature, this same process produces quartz and diamonds. Ultimately, geometry and formations occur in many aspects of nature.
Our end product is an educational video directed towards a younger audience that explains the geometry concepts behind crystal formations and the process in making rock candy. During the video, there is a voice over that plays while pictures and drawing of the crystals appear. For exhibition, we would also like to include rock candy to give out to our audience during the exhibition.
This film presentation will begin with two people debating what to make their math project about, meanwhile eating candy. They then decide that candy can have hidden mathematics, rock candy most of all. These two students make their way to a desktop and begin their research, then coming across a youtube video that teaches the math behind making rock candy. In this film the audience follows the students in their learning and can follow the lesson. The audience can then interact in their own way with getting their own piece of rock candy.
We want our audience to enjoy the presentation itself, and to learn from it that there are hidden mathematics in the making of rock candy. We would also like to inspire them to make some candy of their own. This video will be appealing to all ages, reaching out to a wide array of spectators. This is because we will break down step by step the science and mathematics behind crystal formation and sucrose bonding, then applying that knowledge to formulate why sugar crystals form in the different geometric shapes they do. This new take on candy is a new outlook and will hopefully show our audience that math is applicable to many things that are around in our everyday life, including something as familiar as candy. Throughout this project, our topic and script changed many times but we are very happy with the outcome. Our hope is that our audience will leave with a curiosity for what other daily activities have math hidden concepts in them.
In our first brainstorm, to get inspiration, we created a list of topics that we are interested in and decided that it would be really fun and interesting to do our project on something related to culinary arts. We were aware that there are known sciences, but we were unfamiliar to the mathematics associated with cooking. Our group agreed on making something unique and taking an approach that would grab someone’s attention and so the project began with us researching how math can connect to candy. We stuck with this topic because it is different and appealing to a wide audience. From there, we decided to make something that is kid friendly and interactive, something that would keep spectators entertained.
For our project, we created a two minute video that explains the seven different monoclinic crystal systems. During our first set of research on how rock candy is formed, we came across the mathematical formations of crystals and the relationship it shares with chemistry. We learned about the chemical process in making rock candy, and how evaporation and fractals in crystallization play a key part in the process. From this, we discovered a source called, The Forbidden Crystal Symmetry that describes how geometry is connected to the formation of crystals as well. We explored the geometry formulas behind why the remaining sugar content form the particular crystal like shapes rather than any other shape, specifically fractals in crystallization.
We learned that there are many different stages of solid sugar crystals to a sugar liquid that is used to make hard candy. The stages have varying temperatures and state description. One source that we found very useful is a filmed lecture from www.richannel.org on the structure and geometry of crystals. We learned that there is energy released when they are heated and different sugars react in different ways. From www.curiouscook.com we learned that heat energy makes atoms move faster. As sugar heats up in the pan, its molecules get more and more jittery, to the point that their jitters overcome the attractive forces and they can jump from one set of neighbors to another, meaning it liquefies. We figured out that The change in solubility with change in temperature can be used to create solutions with more solute dissolved than is predicted by the solubility of the substance.
The most helpful website for our research was http://projectsharetexas.org/resource/types-solutions-saturated-supersaturated-or-unsaturate-ontrack-chemistry-module-5-lesson-3 because it defined some important terminology to better understand our topic. There are three solutions that can be given solute and solvent which are unsaturated, saturated and supersaturated. The unsaturated solution does not reach the limit of solubility. The saturated solution has “reached its limit of solubility for a solute at a given temperature”. The supersaturated solution holds “more dissolved solute than it normally would at a given temperature”. This means, by boiling the water and dissolving the sugar, it allows the rock candy solution to cool. If more crystals of the solute are added, they act as seed crystals in nucleation sites for crystal formation. According to Wikipedia, seed crystals are a “small piece of single crystal / polycrystal material from which a large crystal of the same material typically is to be grown. The large crystal can be grown by dipping the seed into a supersaturated solution, into molten material that is then cooled, or by growth on the seed face by passing vapor of the material to be grown over it.” With this information, we further tried to understand the monoclinic crystal formations and the formulas that are involved.
We also learned about crystal lattices, and how when white sugar is heated it breaks off (not breaking down) and separates from it’s crystal bond, forming a liquid. When this liquid cools off, the distance between the individual sugar molecules comes in close again, in the case of making rock candy they hug on the lollipop stick, and they begin to reform they're crystal shape. It is the way they come together, in a unique bond that gives them the distinctive crystal shape. As the candy cools, its contents condense and harden, and the separation goes away as the molecules cling together.
In our project gave a “crash course” of how the mathematics applied in crystal formations. We have found information on the different formations sugars make under certain amounts of heat. Then combining through the cooling process and therefore forming crystals. We also found some resources that explain how crystals take on the geometrical shapes that they do. As a group annotated the formulas to figure out the meaning behind them, then simplified them so they are teachable to a broader audience. Overall, we want our audience to understand the basics of geometry in crystal formation and how it connects to the process in making rock candy. Our script says, “The first thing you will need to know about crystal formation is that there are seven different crystal systems. This includes the triclinic, monoclinic, orthorhombic, tetragonal, trigonal, cubic and hexagonal systems. For this video, we will primarily cover the monoclinic crystal system. The monoclinic system has three unequal axes. The vertical axes are inclined toward each other which creates an oblique angle. The horizontal axis is perpendicular to the other two axes to form a rectangular prism with a parallelogram as its base. These angles are all arranged 90° to each other and are made up of six faces. The monoclinic crystal system is also one of the seven lattice point groups and is described by three vectors. The crystal lattice can be thought of as an array of 'small boxes' infinitely repeating in all three directions. The symmetry properties of the crystal are embodied in its space group. A crystal's structure and symmetry play a role in determining many of its physical properties. Sucrose, for example, starts out with a crystalline structure, specifically in the monoclinic space group. When making rock candy, the sucrose is heated with water to make a supersaturated solution. As it is heated, the crystal lattice structure of the sucrose is disrupted or broken. Once left to cool, the sugar in the solution then begins to crystallize - changing from a liquid to a solid. As the sugar crystals begin to grow; the atoms that make up the sugar align themselves and bond with atoms of the sugar crystal that are growing. Energy is released and the cycle of bonding and growing continues in all directions to once again form a lattice structure but of larger, more pure crystals than the original sucrose. In nature, this same process produces quartz and diamonds. Ultimately, geometry and formations occur in many aspects of nature.
Our end product is an educational video directed towards a younger audience that explains the geometry concepts behind crystal formations and the process in making rock candy. During the video, there is a voice over that plays while pictures and drawing of the crystals appear. For exhibition, we would also like to include rock candy to give out to our audience during the exhibition.
This film presentation will begin with two people debating what to make their math project about, meanwhile eating candy. They then decide that candy can have hidden mathematics, rock candy most of all. These two students make their way to a desktop and begin their research, then coming across a youtube video that teaches the math behind making rock candy. In this film the audience follows the students in their learning and can follow the lesson. The audience can then interact in their own way with getting their own piece of rock candy.
We want our audience to enjoy the presentation itself, and to learn from it that there are hidden mathematics in the making of rock candy. We would also like to inspire them to make some candy of their own. This video will be appealing to all ages, reaching out to a wide array of spectators. This is because we will break down step by step the science and mathematics behind crystal formation and sucrose bonding, then applying that knowledge to formulate why sugar crystals form in the different geometric shapes they do. This new take on candy is a new outlook and will hopefully show our audience that math is applicable to many things that are around in our everyday life, including something as familiar as candy. Throughout this project, our topic and script changed many times but we are very happy with the outcome. Our hope is that our audience will leave with a curiosity for what other daily activities have math hidden concepts in them.