Measure your world
(weebly does not like super/sub-script so some of the equations may look different)
The Measuring Your World is quite a different project. This project was an exploratory-based project where we guide ourselves on many different math concepts. We would learn about the math concept and then do a few problems about to learn how to do them in the future. All the math concepts we learned where we started off with the Pythagorean Theorem, then to the distance formula, and the equation and the unit of a circle. then into trig with sine, cosine, and tangent. we did some more trig with right-triangle trigonometry. The area of polygons and circles. then finally the volumes of common multiple shapes.
The Pythagorean Theorem is the method of finding the length of one side of a right triangle if you know the other two lengths of the triangle. The equation of this is:
a^2 + b^2 = c^2 . The ‘a’ and ‘b’ are the legs of the triangle while ‘c’ is the hypotenuse. As long as you have at least two of the sides you can find the third. This will not work on non right triangles.
Next is the Distance Formula. This formula is used to find the length of a line on a grid and is derived from the Pythagorean Theorem. The equation is:
Distance = (x2 - x1)2 + y2 - y12 . To use this formula you need at least need to know where the two points are for the line. This is similar to the Pythagorean Theorem because you need at least two points of information.
The equation of a circle is (x – h)2 + (y – k)2 = r2. This equation is used for to find the either the radius of a circle or to find where the center of the circle is on a graph. This equation is only for circles on a grid. This relates to the distance formula because sometimes you don't know the radius and you need it to solve the problem. So what you do is find the radius by acting it as a line by itself. Once you do this then you can start the equation of a circle.
The unit circle is just a circle with a radius of one. This circle can be used for many things important. It is mostly used for trigonometry where you divide the circle into 4 parts, then what you could do is put a triangle into any of the four parts and with that can find many measurements of the triangle like the length and angles of it. You must use trigonometry with this.
Sine, Cosine, and Tangent are the main functions of trigonometry and are used to find the length or angles of any part of a right triangle. But first the triangle sides have different functions to them. Hypotenuse is the longest side of the triangle, the Adjacent is where it is right next to the angle that you chose. And the Opposite is the opposite side of the chosen angle.
Sine = opposite over Hypotenuse
Cos = Adjacent over Hypotenuse
Tan = Opposite over Adjacent
The Area of a polygon is to find the area of any polygon starting at five sides. To find the area you split up the polygon into triangles. The more side of the polygon the more triangles there will be. All you have to do now is find the area of one of the triangles by using trigonometry , then take that number and times it by how many sides there are to the polygon. This steps will give you any area of any polygon starting with at least five sides.
The Measuring Your World is quite a different project. This project was an exploratory-based project where we guide ourselves on many different math concepts. We would learn about the math concept and then do a few problems about to learn how to do them in the future. All the math concepts we learned where we started off with the Pythagorean Theorem, then to the distance formula, and the equation and the unit of a circle. then into trig with sine, cosine, and tangent. we did some more trig with right-triangle trigonometry. The area of polygons and circles. then finally the volumes of common multiple shapes.
The Pythagorean Theorem is the method of finding the length of one side of a right triangle if you know the other two lengths of the triangle. The equation of this is:
a^2 + b^2 = c^2 . The ‘a’ and ‘b’ are the legs of the triangle while ‘c’ is the hypotenuse. As long as you have at least two of the sides you can find the third. This will not work on non right triangles.
Next is the Distance Formula. This formula is used to find the length of a line on a grid and is derived from the Pythagorean Theorem. The equation is:
Distance = (x2 - x1)2 + y2 - y12 . To use this formula you need at least need to know where the two points are for the line. This is similar to the Pythagorean Theorem because you need at least two points of information.
The equation of a circle is (x – h)2 + (y – k)2 = r2. This equation is used for to find the either the radius of a circle or to find where the center of the circle is on a graph. This equation is only for circles on a grid. This relates to the distance formula because sometimes you don't know the radius and you need it to solve the problem. So what you do is find the radius by acting it as a line by itself. Once you do this then you can start the equation of a circle.
The unit circle is just a circle with a radius of one. This circle can be used for many things important. It is mostly used for trigonometry where you divide the circle into 4 parts, then what you could do is put a triangle into any of the four parts and with that can find many measurements of the triangle like the length and angles of it. You must use trigonometry with this.
Sine, Cosine, and Tangent are the main functions of trigonometry and are used to find the length or angles of any part of a right triangle. But first the triangle sides have different functions to them. Hypotenuse is the longest side of the triangle, the Adjacent is where it is right next to the angle that you chose. And the Opposite is the opposite side of the chosen angle.
Sine = opposite over Hypotenuse
Cos = Adjacent over Hypotenuse
Tan = Opposite over Adjacent
The Area of a polygon is to find the area of any polygon starting at five sides. To find the area you split up the polygon into triangles. The more side of the polygon the more triangles there will be. All you have to do now is find the area of one of the triangles by using trigonometry , then take that number and times it by how many sides there are to the polygon. This steps will give you any area of any polygon starting with at least five sides.
Design Your Own Project
The Design your own project is a project where we get into a small group and make our own project and solve it. The project had to use any one of the math concepts that were learned with the measure your world course. And the theme and what you were actually measuring were entirely up to us. So in my group we are all doing the rocket intersession next week. In this intersession we will build rockets and launch them in the desert. So we thought we could use this time to also use this as our project. You see when we are going to launch the rockets that we are going to launch are going to go way higher than than any normal method of measuring the the height. So what we are going to do is take a special protractor and flowel the rocket as it goes up. This will give us an angle, and we also know the distance between us and the rocket launch pad. With this information we can use trigonometry to find how high the rocket went.
reflection
for this whole course of Measuring Your World I thought it was very good as in the scene that I learned a lot of new math information in little time. as we went along going to each next math concept it felt like a more changing and different level of a video game. we can use some of the new skills that we learned from last math concept and use them here but we can use them all because how differently they were. with this process it made the coerce not too hard where i was struggling every night and not too easy where I did not learn anything. One of the habits of a mathematician is that he/she is having trouble on the problem they retry the problem with a different approach. This was like me because if I had trouble then I could retry the problem and use one of the solutions from the problem from before.