One of the famous women mathematicians I researched was named Hypatia. Hypatia was not only a mathematician but was also a philosopher and astronomer. She was mostly known in math for inventing an astrolabe for ship navigation to measure the density of fluids. She also did work on algebraic equations and was credited with commentaries on conics (geometry), arithmetic (number theory), and astronomical table. Hypatia loved teaching and leading lectures but back then it was hard to fulfill her dreams because women were not allowed to do those things.

The next mathematician I researched is named Agnesi. Agnesi was also not just a mathematician. She was also philosopher, theologian, and a humanitarian. I found that she was the first woman to do a few things. She was the first women to write a mathematics handbook and was the first women appointed as a math professor at a university. What Agnesi is best known for is the curve called the which of Agnesi the equation of this curve is y=*a*sqrt(*a(x-x))/x. *She believed the x-axis was vertical and y-axis was horizontal. Agnes was credited with writing the first book discussing both differential and integral calculus. She really enjoyed math but math didn’t come first for her it was more of just a hobby.

Now we will move on to the mathematician Noether. Being a mathematician was not the only thing she did. She was also into physics. Her work was mostly in abstract algebra and theoretical physics. Some people know her as the most important women on history of mathematics. Noether developed theories od rings, fields, and algebras which are things I got to learn about in my modern algebra class but I never remember her name coming up in class. Noether also created a theorem, which is, know to be one of the most important theorems in abstract algebra.

Lastly I will talk a little about Kovalevsky. She was the first Russian female mathematician and prior to the 20th century was the best mathematician. She got started in math because she use to study her dads old calculus notes when she was younger and grew to love it. She originally contributed to analysis, partial differential equations, and mechanics. She is a writer and advocator of women rights. Kovalevsky really wanted to lead lectures but was not allowed to due to the fact that she was a woman.

Being able to learn about women in class was inspiring. I never get to learn about what all these different women just about the men. The women do things just as important as the men. So as one of my dailies you bet I was doing some research on more about the women in math. The Internet came up with more then I could have ever imagined. I think in math classes we need to talk more about the women in math that way people don’t see a man sitting behind the math problems they can see men and women. This is what I want to make sure I do as a teacher. Making students aware is one of the best things to do.

]]>Being able to learn about women in class was inspiring. I never get to learn about what all these different women just about the men. The women do things just as important as the men. So as one of my dailies you bet I was doing some research on more about the women in math. The Internet came up with more then I could have ever imagined. I think in math classes we need to talk more about the women in math that way people don’t see a man sitting behind the math problems they can see men and women. This is what I want to make sure I do as a teacher. Making students aware is one of the best things to do.

The fundamental theorem of algebra tells us in short that complex numbers have complex roots with the number of roots being the highest degree in the polynomial. In class we talked about how it was a big deal and the two main reasons that made it such a big deal. The first reason was because it means that numbers are algebraically closed. While this happens it doesn’t mean that integers are closed, because they are not. When you write down a polynomial it is very rare that you will get integers as the solution. You may see this happen but most likely it will not. The second reason it is a big deal is because it means that every polynomial factors into quadratic and linear factors. This means that to understand all polynomials, we need to understand linear and quadratic equations. That should pretty much be second nature to us.

Gauss’ thesis has several proofs but later on they have found some problems in them. Later in his life, he was able to give a good enough proof that satisfied even a modern algebraist. There are not many purely algebraically pure proofs of the fundamental theorem of algebra but Gauss used one neat idea within his proof that we talked about in class. Gauss used Eulers identity to separate polynomials into a real and complex part. In order for Gauss to be able to do this he needed to turn complex numbers from his notation, which was

A specific example follows. We will turn the equation

First we need to make a triangle on an axis using the equation 2+2

In order to find the magnitude we need to use the Pythagorean theorem to find out hypothesis. In case you cant quite remember the Pythagorean theorem is a^2+b^2=c^2 . Since we know *a* and *b* we can use algebra to figure out *c.*

22+22=*c*2

8=*c*2

sqrt(8)=*c*

We know have found our hypotheses which is also our magnitude to be sqrt(8) so we have now found out*r *in the equation we are trying to find.

When going about this part I was really excited because I love algebra and the Pythagorean theorem is just that. When talking about making the triangle I had to remind myself what part of the equation would go where on the triangle but that didn't take long.

22+22=

8=

sqrt(8)=

We know have found our hypotheses which is also our magnitude to be sqrt(8) so we have now found out

When going about this part I was really excited because I love algebra and the Pythagorean theorem is just that. When talking about making the triangle I had to remind myself what part of the equation would go where on the triangle but that didn't take long.

During this proof we got to use multiple parts of math which was awesome.Now its time to find the direction which is θ in our new equations. How we go about finding this is finding the angle in radiant form. How e can find this is using out trig skills of sine, cosine, or tangent better known as s o/h c a/h t o/a. We can use any of these to find out the answer. I am going to use tangent. Since we are trying to find the angle we have the equation.

tan(x)=4/3

Since 4 is our opposite side of the angle and 3 is the adjacent side to the angle. When calculating this we use arctan(4/3) and we obtain π/4. So now we have found our direction which we know is θ in our equation. We now have all the parts we need to be able to put the equation together. Which we get to be sqrt(8)e^(i( π/4)). This is the equation that helped Gauss get through the proof of fundamental theorem of algebra. If you ever read this proof, when it comes to this part you should now be able to understand what is happening and why he does what he does.

While calculation this part it brought me back to when I was learning trigonometry. I will never forget s o/h c a/h t o/a and find it fun to work with. The only thing that was hard for me was when calculating arctan(4/3) making it into radiants of a fraction not just the decimal. I had to try to remember the unit circle we focused on so much in trigonometry. Finally I was able to figure it out. After I found that part the rest was just plug what we needed/found into our equation which is the easiest part.

Working through this part of his proof during class really allowed us to get a feel for things that gauss did and his thinking behind it. It allowed us to be able to see different aspects that go into the fundamental theorem of algebra and how seeing the work behind it better helps us understand it. I believe that this is important in a classroom. In order for kids to really understand what they are doing they need to work through what it is that they are doing and understand why they are doing it.

]]>tan(x)=4/3

Since 4 is our opposite side of the angle and 3 is the adjacent side to the angle. When calculating this we use arctan(4/3) and we obtain π/4. So now we have found our direction which we know is θ in our equation. We now have all the parts we need to be able to put the equation together. Which we get to be sqrt(8)e^(i( π/4)). This is the equation that helped Gauss get through the proof of fundamental theorem of algebra. If you ever read this proof, when it comes to this part you should now be able to understand what is happening and why he does what he does.

While calculation this part it brought me back to when I was learning trigonometry. I will never forget s o/h c a/h t o/a and find it fun to work with. The only thing that was hard for me was when calculating arctan(4/3) making it into radiants of a fraction not just the decimal. I had to try to remember the unit circle we focused on so much in trigonometry. Finally I was able to figure it out. After I found that part the rest was just plug what we needed/found into our equation which is the easiest part.

Working through this part of his proof during class really allowed us to get a feel for things that gauss did and his thinking behind it. It allowed us to be able to see different aspects that go into the fundamental theorem of algebra and how seeing the work behind it better helps us understand it. I believe that this is important in a classroom. In order for kids to really understand what they are doing they need to work through what it is that they are doing and understand why they are doing it.

The book I decided to read for class is called *The Number Mysteries* written by Marcus Du Sautoy. This book was a great read for mathematicians and non-mathematicians. It was all about how math is everywhere in our lives. When I say everywhere, I mean literally everywhere. We use math daily and many times do not even realize when we are using it. The author gave us some specific math tips and left a million dollar questions for us to try and solve at the end of each chapter. I will reflect on the five chapters in this book with what they were about and how it helps us shape the math world.

Chapter one was called the curious incident of the never-ending primes. This chapter, as you could probably guess, is all about primes. He questioned why a lot of star soccer players wear prime numbers and if prime number out on a field would make the team win. This was weird to me because if everyone on the field was wearing a prime number, how would that make them play better. He talked about how primes are in music, specifically rhythms and chords. Primes are everywhere and even though some people might not technically know what a prime number is they see it and could even use it daily.

Chapter two was called the story of the elusive shape. This chapter was interesting. Have you ever wondered why if you blew bubbles with a square frame it still comes out as a sphere? I know I have. Well its because nature is lazy. The reason nature picks a sphere is because a sphere is the shape that requires the least amount of energy. This chapter talks about what the best shape for packing is and how nature knows all this. Which seems crazy. You look at nature and everything is the way it is for a reason. It is not just random. Everything has a purpose from the way leaves are shaped to the way snowflakes are shaped. Shapes are everywhere and everything has a shape.

Chapter three is called the secret of the winning streak. This chapter really allowed you to see different kinds of math in things we do for fun and things you did not know could require math to help win. The first game that everyone loves that it talked about was rock paper scissors. For this game, it is all about patterns. Usually when players play this game they can latch on to a pattern of doing rock a lot so when you see this pattern act right away with the wining move. Your best bet to win rock paper scissors is to be very inconsistent with what you pick. In this chapter it also talked about how to win at games like poker, the lottery, and roulette. It was a lot about probability and it went deeper into the math but for me I tended to get lost and confused in the math. If you want to know the math behind winning these games you should check this book out.

Chapter four is called the case of the uncrackable code. Codes are everywhere. English is a code made up of 26 alphabetical letters. Some well known albums have Morse code on them like one of Coldplay’s albums and one of The Beetles albums. When you buy something online your credit card gets sent to the store as a code, which makes it harder for hackers to get your credit card number. This chapter also talks about the clock calculator. This of course is modulo. Our clock is in modulo 12 and we use it everyday. If you asked a random person what modulo 12 is they would have no idea what that means but they use it everyday. That how they know if they took a nap at 9 and woke up 4 hours later the time is 1 not 13.

Chapter five is called the quest to predict the future. This chapter talked about how being able to predict the future relies on math. The reason we can predict when things like when solar eclipses are going to happen is because of the pattern of them previously happening. We now know that eclipses happen every 19 years. This is just the start. We can see these patterns in nature as well and can predict things about plants and animals. In this chapter it also talked about Galileo and how he tries to predict something about to same shaped soccer balls with heavier masses. Most people would think that if you had two soccer balls one filled with cement and the other one with air that the one filled with cement would fall faster but that’s not true. They actually both fall at the same time. If you don’t believe me test it for yourself!

Overall this book was a great read. Some parts lost me but it was actually really interesting being able to actually see how they are doing the math. This book opened up my eyes to actually how much we see and use math on a day-to-day basis. Math is everywhere. Plus if you are really interested in certain chapters you can always try to figure out the million dollar questions and become a millionaire. I would definitely recommend this book to everyone if they want to be intrigued with mathematics.

]]>Chapter one was called the curious incident of the never-ending primes. This chapter, as you could probably guess, is all about primes. He questioned why a lot of star soccer players wear prime numbers and if prime number out on a field would make the team win. This was weird to me because if everyone on the field was wearing a prime number, how would that make them play better. He talked about how primes are in music, specifically rhythms and chords. Primes are everywhere and even though some people might not technically know what a prime number is they see it and could even use it daily.

Chapter two was called the story of the elusive shape. This chapter was interesting. Have you ever wondered why if you blew bubbles with a square frame it still comes out as a sphere? I know I have. Well its because nature is lazy. The reason nature picks a sphere is because a sphere is the shape that requires the least amount of energy. This chapter talks about what the best shape for packing is and how nature knows all this. Which seems crazy. You look at nature and everything is the way it is for a reason. It is not just random. Everything has a purpose from the way leaves are shaped to the way snowflakes are shaped. Shapes are everywhere and everything has a shape.

Chapter three is called the secret of the winning streak. This chapter really allowed you to see different kinds of math in things we do for fun and things you did not know could require math to help win. The first game that everyone loves that it talked about was rock paper scissors. For this game, it is all about patterns. Usually when players play this game they can latch on to a pattern of doing rock a lot so when you see this pattern act right away with the wining move. Your best bet to win rock paper scissors is to be very inconsistent with what you pick. In this chapter it also talked about how to win at games like poker, the lottery, and roulette. It was a lot about probability and it went deeper into the math but for me I tended to get lost and confused in the math. If you want to know the math behind winning these games you should check this book out.

Chapter four is called the case of the uncrackable code. Codes are everywhere. English is a code made up of 26 alphabetical letters. Some well known albums have Morse code on them like one of Coldplay’s albums and one of The Beetles albums. When you buy something online your credit card gets sent to the store as a code, which makes it harder for hackers to get your credit card number. This chapter also talks about the clock calculator. This of course is modulo. Our clock is in modulo 12 and we use it everyday. If you asked a random person what modulo 12 is they would have no idea what that means but they use it everyday. That how they know if they took a nap at 9 and woke up 4 hours later the time is 1 not 13.

Chapter five is called the quest to predict the future. This chapter talked about how being able to predict the future relies on math. The reason we can predict when things like when solar eclipses are going to happen is because of the pattern of them previously happening. We now know that eclipses happen every 19 years. This is just the start. We can see these patterns in nature as well and can predict things about plants and animals. In this chapter it also talked about Galileo and how he tries to predict something about to same shaped soccer balls with heavier masses. Most people would think that if you had two soccer balls one filled with cement and the other one with air that the one filled with cement would fall faster but that’s not true. They actually both fall at the same time. If you don’t believe me test it for yourself!

Overall this book was a great read. Some parts lost me but it was actually really interesting being able to actually see how they are doing the math. This book opened up my eyes to actually how much we see and use math on a day-to-day basis. Math is everywhere. Plus if you are really interested in certain chapters you can always try to figure out the million dollar questions and become a millionaire. I would definitely recommend this book to everyone if they want to be intrigued with mathematics.

When asking people what a number is, people have a variety of different responses. Who is to say they are wrong or right? There are so many different things numbers do that just one sentence cannot even begin to sum it all up. It crazy that’s such a simple word can have so much complexity within it.

In class we were asked to come up with a sentence that we thought best described the word number. After we had a few minutes to come up with one we were asked at our table to come up with one sentence we all could agree on. After that, each table wrote their sentence on the board. No two sentences were the same. After all of the different sentence were on the board we all realized that there are so many different elements that go into what a number is. One group’s sentence was something giving quantity to an object or itself. The second group’s sentence was a value that’s a distance from zero. The third group’s sentence was a symbol that represents and amount. The last group’s sentence was something that carries meaning to the size of the set.

So which sentence best describes a number? It was time to put these sentences to the test. What’s a better test then actually using real numbers to see if it holds true. We needed to pick different numbers to see if it holds true for all types so we picked 0, -2, 1/3, , infinity. There were two sentences the whole class found to be right, those being a value that’s a distance from zero and a symbol that represents an amount. We found the other two sentences were wrong because something giving quantity to an object or itself was confusing to people and felt that it might not work for infinity. Then for the other sentence that was something that carries meaning to the size of the set we said did not work for -2 because if we think about it someone cannot have negative two apples. So as we can see that everyone might have an opinion about what a number is but to see if it is really true or not we need to test it. Since there is no one true definition of a number and we can have multiple ones since so much goes into a number testing it is the only way.

In class we were asked to come up with a sentence that we thought best described the word number. After we had a few minutes to come up with one we were asked at our table to come up with one sentence we all could agree on. After that, each table wrote their sentence on the board. No two sentences were the same. After all of the different sentence were on the board we all realized that there are so many different elements that go into what a number is. One group’s sentence was something giving quantity to an object or itself. The second group’s sentence was a value that’s a distance from zero. The third group’s sentence was a symbol that represents and amount. The last group’s sentence was something that carries meaning to the size of the set.

So which sentence best describes a number? It was time to put these sentences to the test. What’s a better test then actually using real numbers to see if it holds true. We needed to pick different numbers to see if it holds true for all types so we picked 0, -2, 1/3, , infinity. There were two sentences the whole class found to be right, those being a value that’s a distance from zero and a symbol that represents an amount. We found the other two sentences were wrong because something giving quantity to an object or itself was confusing to people and felt that it might not work for infinity. Then for the other sentence that was something that carries meaning to the size of the set we said did not work for -2 because if we think about it someone cannot have negative two apples. So as we can see that everyone might have an opinion about what a number is but to see if it is really true or not we need to test it. Since there is no one true definition of a number and we can have multiple ones since so much goes into a number testing it is the only way.

Now lets think about infinity. In our example above we used infinity as a number to test if our number definition worked with infinity or not but is infinity even a number? This is another discussion we had in class. What is infinity and is it a number? We said the definition of infinity is something that keeps going on from either direction. Examples we thought of were a line or like numbers. The class mostly agreed with this, but in this definition we are saying that infinity is not exactly a number. What if I said infinity can act as a number though. We can treat infinity like a number but it can change. Therefore we agreed that it is not a number but it has qualities like a number, which then would allow us to use it like a number in our example in the last paragraph.

When talking about numbers and infinity it gets kind of crazy. I say this because a lot of people know about and use numbers and infinity in everyday life, especially in math, but when trying to put a definition to the words or describe what it is we find it difficult. We know what they both do and act like but cannot pinpoint a specific definition for them. Doing this activity really opened my eyes to how something so big in our lives as math majors can conclude a wrong definition for something like numbers. Its a big concept but asking anyone else if they think math majors would know what a number was my guess is there response would be I sure hope so. These people might not know how complicated the number system can actually get. With doing this activity in my classroom I would love to incorporate something along these lines so students can see and understand how many different pieces of the math puzzles goes into something like numbers. This can open their eyes to how we need to test things to make sure a definition actually fits what we are talking about and just how there are things behind the scenes that we can explore. There are so many things we do in math just because we know we can such as why a negative times a negative is a positive. Being able to explain why and explore this with my class is a great way for them to think deeper and to be able to get the full picture.

]]>When talking about numbers and infinity it gets kind of crazy. I say this because a lot of people know about and use numbers and infinity in everyday life, especially in math, but when trying to put a definition to the words or describe what it is we find it difficult. We know what they both do and act like but cannot pinpoint a specific definition for them. Doing this activity really opened my eyes to how something so big in our lives as math majors can conclude a wrong definition for something like numbers. Its a big concept but asking anyone else if they think math majors would know what a number was my guess is there response would be I sure hope so. These people might not know how complicated the number system can actually get. With doing this activity in my classroom I would love to incorporate something along these lines so students can see and understand how many different pieces of the math puzzles goes into something like numbers. This can open their eyes to how we need to test things to make sure a definition actually fits what we are talking about and just how there are things behind the scenes that we can explore. There are so many things we do in math just because we know we can such as why a negative times a negative is a positive. Being able to explain why and explore this with my class is a great way for them to think deeper and to be able to get the full picture.

The Sumerians used tessellations with building wall decorations around 4000 BC. These decorations were formed by patterns of clay tiles. In 1619, Johannes Kepler studied tessellations. In his book Harmonicies Mundi, he was the first to explain the hexagonal structures of honeycomb and snowflakes. In 1891 Yevgraf Fyodorov proved that every periodic tilling contains one of seventeen different groups of isometries. With Fyodorov proving this, it unofficially began the mathematical study of tessellations. The start of the tessellation era led us to tiling on walls with clay but now we have realized we can do them anytime anywhere and how beautiful they look. They have been around for thousands of years and are here to stay forever which is great for me considering I cannot wait to teach my students about tessellations.

In class I started out using pattern blocks. Giving students the option to use all different sorts of manipulates allows their mind to run free with what they are wanting to create. When pulling out the pattern blocks there were a few things I had to remember and look for. I needed to look for shapes that went together without overlapping and leaving no gaps. This really let me explore my options. Another thing I needed to keep in mind was that I needed a pattern. So I can’t just put all these random shapes together. I needed to create something cool out of the shapes then remake it over and over again creating a tessellation. Below is the tessellation I created in class.

One big thing I notice when looking over the tessellation I came up with is that it is based off of hexagons. I started off with one yellow hexagon in the middle. Since I choose this to be my center shape my whole creation will be base off of that making every shapes the shape of a hexagon. Next I wanted to use red trapezoids. The trapezoids fit around the hexagon perfectly making a bigger hexagon around my centerpiece. I wanted to use one more shape to make it bigger. I really wanted to use orange squares. So I started putting squares where they fit above each trapezoid but then I noticed there were gapes in between every two squares. I had two options. One was to not use squares and try to find another shape that would not leave any gaps or I could find a shape to fill in the gaps between the squares. I choose the second option. As you can see I found a shape that fit perfectly in the space and it ended up being a triangle! Once again I noticed right away that the squares and triangles make an even bigger hexagon. Meaning this shape was all centered around the center piece I had chosen. After I found my main shape out of all my blocks I had to make it a tessellation by doing the same thing over again and connecting each big piece where they fit so its like we are translating the shape. I only did four big pieces but feel free to keep going and adding as many big pieces as you can.

I went home and for our daily homework I really wanted to create another tessellation so I did just that. I got out isometric cubed paper and started creating. What I came up with is pictured below.

I went home and for our daily homework I really wanted to create another tessellation so I did just that. I got out isometric cubed paper and started creating. What I came up with is pictured below.

I started off with a column of just light blue rhombuses. On this isometric cubed paper it also looks like two triangles when their bases touching each other. Then in the next column I decided to use more rhombuses but they are just turned differently so that they fit along the side of the previous column of rhombuses. I alternated the colors of rhombuses in this Column. Then I did another column of light blue rhombuses. Then I decided to add one more row of the rhombuses turned differently but I alternated the colored the opposite way to give me another line of the pattern. Once I had my four steps done I then kept repeating the pattern until the paper was all used up. We can also look at this pattern another way. If you look at a point where two of the light blue rhombuses touch and look at all the other rhombuses that meet at that point we can see that we are just rotating each rhombus 60 degrees still using the same pattern of colors around that one shape. This tessellation was based on just using one shape and that’s okay to do we just have to make sure we follow a pattern. Using this isometric cubes paper we can see the triangles within the rhombuses showing us that instead of using rhombuses for every row we could have used triangles for a row or two.

This is a great activity for students. They get to integrate art within math. There are a couple of big things students get to see within doing this activity, those things being reflection, rotation, and translation. Just like with my second tessellation we found it had rotation and kids will be able to see these things after they are done without even realizing they have done so. This activity also allows students to explore different geometric shapes along with the shapes that can be made using other shapes just like in my first tessellation I had trapezoids, triangles and squares making a hexagon. This is not only a fun activity for the classroom but a very beneficial one as well. I am looking forward to working on tessellations with my students when I get a classroom of my own.

]]>This is a great activity for students. They get to integrate art within math. There are a couple of big things students get to see within doing this activity, those things being reflection, rotation, and translation. Just like with my second tessellation we found it had rotation and kids will be able to see these things after they are done without even realizing they have done so. This activity also allows students to explore different geometric shapes along with the shapes that can be made using other shapes just like in my first tessellation I had trapezoids, triangles and squares making a hexagon. This is not only a fun activity for the classroom but a very beneficial one as well. I am looking forward to working on tessellations with my students when I get a classroom of my own.

Math was a big part of our history and is still a big part of our culture today. What these famous mathematicians founded back long ago are things we still use today and things that if they hadn’t been founded then math could be completely different. What these guys have found has helped us be able to use things like theorems or equations to solve different aspects of math in today’s world. So far in class we have talked about the Greek mathematicians. These include Euclid, Thales, Pythagoras, and Archimedes. They all did multiple things to contribute to our math world today but I will talk about a few big things they have done for us and why they are so important.

First we will talk about Euclid. The big thing Euclid did for math was he came up and proved many propositions to help us be able to say certain things about numbers, lines, and shapes. Also these propositions or theorems are things we can use to be able to prove other theorems. They build off of each other and without this foundation of propositions it would make a mathematicians life a lot harder because they would have to re prove everything instead of just using these propositions that have already been proven true. In class we looked at some of this propositions. Back when he wrote them their language was much different with how they worded things so reading and really understanding what each proposition is saying is a job in its self. During class we got to look at them and word them so that they made more sense to us!

Next we will talk about Thales. Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. There is such a thing called the Thales theorem, which allowed us to prove and say something about triangles inside of a circle that goes through the diameter of the circle. He has been known as the first true mathematician. He later proved other foundational results to help us be able to conclude about things in geometry. Such as; a circle is bisected by any of its diameters, the angles at the base of an isosceles triangle are equal, when two straight lines cut each other the vertically opposite angles are equal, and two triangles are equal in all respects is they have two angles and one side respectively equal. Without these foundations it would make geometry harder for us to prove the bigger picture theorems. These foundations allow us to use them when proving theorems. Once again without these our life with proving theorems would be that much harder.

Now we will talk about Pythagoras. The big thing Pythagoras did in math is something I’m sure everyone has herd about, the Pythagorean theorem. Being able to use this in math allowed us to be able to find side lengths of a right triangle with the equation. Without the creation of the Pythagorean theorem finding side length would have to deal with using things like squares to find each side length like Pythagoras had to in order to create and prove this theorem. It would be a much longer process. In class we got to look up and pick out facts about Pythagoras. There were many funny things true and untrue about him on the Internet. Our class found things like; his followers didn’t eat bean, he sacrificed 100 oxen to prove this theorem, his follower’s motto was all is a number, and that he could fly. I’m sure you could guess what ones were fictions and which were not. I know that the discovery of the Pythagorean theorem has helped me through many math classes.

Lastly we will talk about Archimedes. Archimedes is said to be one of the greatest geniuses our species has produced. He is known for the relationship he discovered and proved between the volume of a sphere and a circumscribed cylinder. Without this prove we obviously wouldn’t have the relationship between the two or the prove that goes with it. We looked at this prove in class and let me tell you what. This man was a genius. The things he did still makes me confused. It’s a hard prove to follow but once you break it down it starts to make sense. How he came up with these things is beyond me and incredible. Even just looking at his diagram you get lost. There are triangles, circles, and spheres all over. In order for him to prove this, his knowledge of circles and triangles must have been like the back of his hand to him. He was a very smart man and helped out the math world in many ways.

Overall these four guys we have talked about in class so far I think are all geniuses. Without these guys and the things they have accomplished math could be very different or someone else could have discovered these things but we will never know. We also don’t know what else is out there that is just waiting to be discovered. These discoveries let us conclude different things in math. Also they allowed us to use these discoveries to show and prove other theorems. I think everyone now a day is happy someone discovered these things to make our math life a little easier and definitely more fun. Being able to use other theorems is like a big puzzle and we have to find the pieces that go together to give us what we want. It was amazing being able to learn more about these four guys and I cant wait to see who else we get to learn about in this class.

]]>First we will talk about Euclid. The big thing Euclid did for math was he came up and proved many propositions to help us be able to say certain things about numbers, lines, and shapes. Also these propositions or theorems are things we can use to be able to prove other theorems. They build off of each other and without this foundation of propositions it would make a mathematicians life a lot harder because they would have to re prove everything instead of just using these propositions that have already been proven true. In class we looked at some of this propositions. Back when he wrote them their language was much different with how they worded things so reading and really understanding what each proposition is saying is a job in its self. During class we got to look at them and word them so that they made more sense to us!

Next we will talk about Thales. Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. There is such a thing called the Thales theorem, which allowed us to prove and say something about triangles inside of a circle that goes through the diameter of the circle. He has been known as the first true mathematician. He later proved other foundational results to help us be able to conclude about things in geometry. Such as; a circle is bisected by any of its diameters, the angles at the base of an isosceles triangle are equal, when two straight lines cut each other the vertically opposite angles are equal, and two triangles are equal in all respects is they have two angles and one side respectively equal. Without these foundations it would make geometry harder for us to prove the bigger picture theorems. These foundations allow us to use them when proving theorems. Once again without these our life with proving theorems would be that much harder.

Now we will talk about Pythagoras. The big thing Pythagoras did in math is something I’m sure everyone has herd about, the Pythagorean theorem. Being able to use this in math allowed us to be able to find side lengths of a right triangle with the equation. Without the creation of the Pythagorean theorem finding side length would have to deal with using things like squares to find each side length like Pythagoras had to in order to create and prove this theorem. It would be a much longer process. In class we got to look up and pick out facts about Pythagoras. There were many funny things true and untrue about him on the Internet. Our class found things like; his followers didn’t eat bean, he sacrificed 100 oxen to prove this theorem, his follower’s motto was all is a number, and that he could fly. I’m sure you could guess what ones were fictions and which were not. I know that the discovery of the Pythagorean theorem has helped me through many math classes.

Lastly we will talk about Archimedes. Archimedes is said to be one of the greatest geniuses our species has produced. He is known for the relationship he discovered and proved between the volume of a sphere and a circumscribed cylinder. Without this prove we obviously wouldn’t have the relationship between the two or the prove that goes with it. We looked at this prove in class and let me tell you what. This man was a genius. The things he did still makes me confused. It’s a hard prove to follow but once you break it down it starts to make sense. How he came up with these things is beyond me and incredible. Even just looking at his diagram you get lost. There are triangles, circles, and spheres all over. In order for him to prove this, his knowledge of circles and triangles must have been like the back of his hand to him. He was a very smart man and helped out the math world in many ways.

Overall these four guys we have talked about in class so far I think are all geniuses. Without these guys and the things they have accomplished math could be very different or someone else could have discovered these things but we will never know. We also don’t know what else is out there that is just waiting to be discovered. These discoveries let us conclude different things in math. Also they allowed us to use these discoveries to show and prove other theorems. I think everyone now a day is happy someone discovered these things to make our math life a little easier and definitely more fun. Being able to use other theorems is like a big puzzle and we have to find the pieces that go together to give us what we want. It was amazing being able to learn more about these four guys and I cant wait to see who else we get to learn about in this class.

I don’t know much about the biggest milestones in math but I know some pretty important people were Euclid, Fibonacci, and Euler. That is all I really know about the history is the names and a little about what they did or came up with. I am looking forward to learning more about the history and milestones of the math world.

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