# coordinates

2021/4/6 Topic: Discussion Week 9 This is a graded discussion: 20 points possible due Apr 6 34 45 Discussion Week 9 Initial Post Make your initial post by Tuesday 11:59 pm In your own words describe why we change coordinates? Why do we use Polar, Cylindrical, Spherical, and Rectangular? What are there uses? You could add a link to an application you might find online. Peer Responses Respond to at least two peers by Thursday 11:59 pm Respond to at least two of your peers, and comment on their application. Do you agree with their reasoning for the coordinate systems or just something you find interesting Please remember proper netiquette…make sure your responses to your peers are polite. Thank you! Resources Canvas guides and supplemental resources are provided to help you complete each activity. How do I reply to a discussion? (https://community.canvaslms.com/docs/DOC-10561-4212190706) Grading Rubric Please see the grading rubric for guidance on what is expected for full credit. Click the snowman icon (3 vertical dots), then select “Show Rubric.” Search entries or author Unread https://sdccd.instructure.com/courses/2417891/discussion_topics/14550642?module_item_id=41176631 Subscribe 1/25 2021/4/6 Topic: Discussion Week 9 Reply (https:// Johnathan Pham (He/Him) (https://sdccd.instructure.com/courses/2417891/users/8706519) Mar 27, 2021 We change coordinates because particles like to move from one coordinate of one location to a different coordinate from another location. We use polar coordinates because polar coordinates use a distance and direction to describing where the position is located. Polar coordinates are used to avoid collisions between other ships, because it is used in ship navigation for the destination or direction of travel, and this can be given as an angle and distance between other ships to avoid collisions. We use cylindrical coordinates because cylindrical coordinate is needed to find the location of a point in space and it is useful to find cylindrical coordinates in objects that have some rotational symmetry in a longitudinal axis. Cylindrical coordinates are used for heat distribution in a metal cylinder because the cylindrical coordinates for the heat distribution in a metal cylinder have rotational symmetry in a longitudinal axis. We use spherical coordinates because it is similar to polar coordinates, but it is used to create a new three-dimensional coordinate system. Spherical coordinates are used in spherical robots because it is a robot with two rotary axes and one linear axis, and the spherical robots have an arm which forms a spherical coordinate system. We use rectangular coordinates because rectangular coordinates find points in a plane using ordered pairs of the coordinates (x,y). Rectangular coordinates are used to locate precise locations on a graphed map. Edited by Johnathan Pham (https://sdccd.instructure.com/courses/2417891/users/8706519) on Apr 1 at 5:35am (http Angie Padua (https://sdccd.instructure.com/courses/2417891/users/8701792) Mar 29, 2021 Hello Johnathan, We had some similar responses. I like your example of polar coordinates used to avoid collisions between other ships. It is true without the use of polar coordinates ships would have a hard time navigating in the ocean because it looks the same in every direction if there was no land around to use as landmarks. I was thinking aircraft, but found out they use a slightly modified version of the polar coordinates. I never thought about the spherical robot arm having two rotary axis and liner axis. I looked it up and saw the use of the arm. You https://sdccd.instructure.com/courses/2417891/discussion_topics/14550642?module_item_id=41176631 2/25 2021/4/6 Topic: Discussion Week 9 used a really great explanation for the use of spherical coordinate. This was a pretty neat area to research for real life use. (http Thao Chung (https://sdccd.instructure.com/courses/2417891/users/8705133) Mar 30, 2021 Hi Johnathan, I like the way how you mention and explain the uses of each coordinate system. It is short but enough information for us to understanding. I am interested in the Polar coordinates are used to avoid collisions between other ships. It’s super exciting and wonderful when using the marine map. It is like the chessboard where the polar coordinate system is used the most to determine the position of the ship also to help the sailors find the right direction to go. Wonderful Thank you so much for sharing Johnathan. (http Emily Warren-Birkholz (https://sdccd.instructure.com/courses/2417891/users/8706378) Sunday Hi Jonathan! I liked how thorough you explanation of each coordinate system was while also being to the point. I would say we had pretty similar responses to the questions so I definitely agree with your responses. I think rectangular coordinates are my personal favorite out of all of them. Thanks for your great contribution to the discussion! Best, Emily (http Kyle Maddox-Gomez (https://sdccd.instructure.com/courses/2417891/users/8714908) Yesterday Hi Johnathan, You define each coordinate system in a way that is easy to understand as well as give interesting application examples that helped me learn something new. I personally was taught how to use the polar coordinate system when I was younger and still in boy scouts. They taught us how to perform basic land navigation using a compass and utilizing a distance needed to travel and the directional angle to walk in. https://sdccd.instructure.com/courses/2417891/discussion_topics/14550642?module_item_id=41176631 3/25 2021/4/6 Topic: Discussion Week 9 Reply (https:// Angie Padua (https://sdccd.instructure.com/courses/2417891/users/8701792) Mar 29, 2021 We change coordinates so that we can have a convenient way to describe a position of an object, or location of points in space. The different types of coordinates have different types of equations to solve problems. Polar coordinates are useful way to describe the location of a point in a plane, particularly when using circles. Polar coordinates are used in animation particularly when using arcs and in areas for animating live creatures. In three dimension the coordinate system is called cylindrical coordinates. Cylindrical coordinates are useful for dealing with problems involving cylinders, like when calculating the volume of a round water tank or the amount of water flowing through a pipe. This coordinate is commonly used in physics when studying electrical charges. There are two distances (r and z) and one angle measure (θ) when describing the point in a space. Spherical coordinates are useful for dealing with problems involving spheres like finding the volume of domes structures. There are one distance (ρ) and two angles (θ an ϕ). An example of when this is used is when you define the location of a state on Earth’s surface, we use longitude and latitude. Rectangular coordinates are cartesian coordinate systems in two dimensions. We use this to identify location such as by drawing points on a map vertically and horizontally precise location marks can be made with coordinates like (-3,2) depending on location of the point on a grid which would allow for an accurate map marking. (http Johnathan Pham (He/Him) (https://sdccd.instructure.com/courses/2417891/users/8706519) Mar 30, 2021 Hi Angie, I found something interesting about your explanation of the cylindrical coordinates for the round water tanks is a way to find if a object has cylindrical coordinates is if it has rotational symmetry in two dimensional, and if it has a translation symmetry. For the spherical coordinates I like your Earth’s surface example because it has a rotational symmetry in all three dimensions around Earth. I remember seeing polar coordinates to do some animations like circles, ellipses, spirals. Having polar coordinates equations makes it easier to get https://sdccd.instructure.com/courses/2417891/discussion_topics/14550642?module_item_id=41176631 4/25 2021/4/6 Topic: Discussion Week 9 curves and this has the ability to do movement patterns like shot patterns, reviving a spaceship, and splash damage from a spaceship verse alien app. Edited by Johnathan Pham (https://sdccd.instructure.com/courses/2417891/users/8706519) on Mar 30 at 8:57pm (http Thao Chung (https://sdccd.instructure.com/courses/2417891/users/8705133) Mar 30, 2021 Hi Angie, You did very great Angie. It is clear and easy to understand. I found some similar ideas from your response. I definitely agree with you that we have several types of coordinate systems in which different ways to use that’s why we have to find the most convenience also as easiest way to work with the problem and solve it quickly. I think those coordinate systems we learn have there is one thing in common that helps us to find the position and distance of the point from the axis. I like how you mention to the Earth’s surface that we use longitude and latitude. Thank you so much for sharing Angie!!! (http Daniel Lee (https://sdccd.instructure.com/courses/2417891/users/8851049) Thursday Hello Angie, I like your response, and it looks pretty interesting to read overall. I had a hard time trying to figure out what the different types of coordinates are used for, so your examples helped me understand a lot. I like how you used latitude and longitude to describe the spherical coordinates. I also like how you used the two examples of the pipe and the tank to describe the cylindrical coordinates. This type of coordinate was the hardest for me to understand, but it seems like that it is used where the z value is not curved as in a polar coordinate. Thank you for your post, and I hope to see more from you in future discussions. (http Lauren Mutchler (https://sdccd.instructure.com/courses/2417891/users/8818976) Friday Hi Angie, thank you for your great post! I love how simple your definitions are because they are easier to understand. I was having a hard time fully comprehending everything and you did a great job at explaining. I had some similar examples as you so that’s good. I appreciate your great response and I agree with all of your definitions and applications. (http Hanyue Duan (https://sdccd.instructure.com/courses/2417891/users/8712670) https://sdccd.instructure.com/courses/2417891/discussion_topics/14550642?module_item_id=41176631 5/25 2021/4/6 Topic: Discussion Week 9 3:32am Hi Angie, Very good understanding, your understanding and application of the replacement of coordinate systems and various coordinates are very in place. Each coordinate system has its own advantages and disadvantages, so that the reasonable use of the coordinate system in display and practical applications can solve the problem well. Reply (https:// Thao Chung (https://sdccd.instructure.com/courses/2417891/users/8705133) Mar 30, 2021 We change the coordinates just to use an easier way to find the position of the point in planes also to find the distance from this point to the axis. We have 4 different types of coordinates that we can use to find the point’s position which are Polar, Cylindrical, Spherical and Rectangular coordinates systems. Polar Coordinate: any point on the plane is determined by its radial distance from the origin known as position and an angle theta known as radian. The angle is always measured from the x-axis to the radial line from the origin to the point. In the same way that a point in Cartesian coordinates is defined by a pair of coordinates (x,y), in radial coordinates, it is defined by the pair (r, 𝜃 ). Cylindrical coordinates are more straightforward to understand than spherical and are similar to the three-dimensional Cartesian system (x,y,z). In this case, the orthogonal x-y plane is replaced by the polar plane and the vertical z-axis remains the same. The conversion between cylindrical and Cartesian systems is the same as for the polar system, with the addition of the z coordinate. Spherical coordinates define the position of a point by three coordinates rho (𝜌 ), theta (𝜃 ), and phi (𝜙 ). 𝜌 is the distance from the origin which is similar to in polar coordinates is the same as the angle in polar coordinates and is the angle between the -axis and the line from the origin to the point. In the same way as converting between Cartesian and polar or cylindrical coordinates, it is possible to convert between Cartesian and spherical coordinates. https://sdccd.instructure.com/courses/2417891/discussion_topics/14550642?module_item_id=41176631 6/25 2021/4/6 Topic: Discussion Week 9 Rectangular coordinates are used to get to a specified point. It starts at the origin, travels along the x-axis the distance specified by the first coordinate, then parallel to the y-axis according to the second coordinate, and then up parallel to the z-axis according to the third coordinate. (http Johnathan Pham (He/Him) (https://sdccd.instructure.com/courses/2417891/users/8706519) Thursday Hi Thao, What I found interesting about rectangular coordinates is that it is seen in a lot of places just like houses. My first time I learned about rectangular coordinates was when I was a six-yearold I used to play at home with a small clay ball and I used three pencils used it to poke three holes in it. My parents explained to me that this relates to rectangular coordinates because each pencil can have its own point connecting to the clay ball, and my teacher helped me measure and label each side of the pencil using a ruler. I had fun learning about rectangular coordinates because I was explained by a lot of my math teachers during elementary school. My parents told me when I was in fifth grade when I visited my friend’s house, they explained to me the house is a real-life application example of rectangular coordinates. I grew up and learned more about rectangular coordinates like the floor of the house has the xy-plane, the wall with the window can be the xz-plane and the wall with the door is the yz-plane, then I played a game Cat and mouse, and Spinning tops with my family, and friends for the whole day. Edited by Johnathan Pham (https://sdccd.instructure.com/courses/2417891/users/8706519) on Apr 1 at 11:16am (http Daniel Lee (https://sdccd.instructure.com/courses/2417891/users/8851049) Thursday Hello Thao, I really enjoyed reading your post. I especially liked it when you described how cylindrical coordinates are more simpler than the spherical coordinates. It seems like in spherical coordinates, the third variable is defined by an angle instead of just a function. I also like how you explained the rectangular coordinates as traveling parallel to a specific axis for each variable. There are a lot of situations where these coordinates can be used, because most situations do not involve objects with curved sides and instead, only polygons are involved. It seems like this type of coordinate is very simple to understand because they can be expressed using straight lines. Thank you for your post! https://sdccd.instructure.com/courses/2417891/discussion_topics/14550642?module_item_id=41176631 7/25 2021/4/6 Topic: Discussion Week 9 Reply (https:// Daniel Lee (https://sdccd.instructure.com/courses/2417891/users/8851049) Thursday We change coordinates in order for a region or a point on the graph to be represented in an easier way so that the distance between a point and an axis can be easily determined. Polar coordinates are used to describe a point on a 2 dimensional graph using distance from the origin and direction of the angle, and are most commonly used in a round-shaped area. They are used in the real world in the case of using radar within a specific radius, such as in air traffic control, where anything in the air nearby is monitored and described using these coordinates. Cylindrical coordinates are used for describing a point on a 3D graph using the same method as polar coordinates, and also has a height that remains unchanged by the conversion. They can be used in the real world in the case of any cylindrical area, such as finding the volume of a gas holder. Spherical coordinates are used to describe a point on 3D graph using a similar method as polar and cylindrical coordinates, but the height is changed by the conversion. They can be used in the real world in the case of any spherical area, such as using coordinates to express the location of a specific crater or mountain on a different planet. Rectangular coordinates are used for finding a specific point in a graph. They are specified using the 3 values of the closest distances between the point and the yz, xz, and xy planes. Edited by Daniel Lee (https://sdccd.instructure.com/courses/2417891/users/8851049) on Apr 1 at 2:55pm (http Lauren Mutchler (https://sdccd.instructure.com/courses/2417891/users/8818976) Friday Hi Daniel. I agree with all of your definitions and applications. I really like the applications you chose like the gas holder and the location of a crater or planet. You did a great job at explaining everything. Thank you for your post! (http Angie Padua (https://sdccd.instructure.com/courses/2417891/users/8701792) Friday https://sdccd.instructure.com/courses/2417891/discussion_topics/14550642?module_item_id=41176631 8/25 2021/4/6 Topic: Discussion Week 9 Hello Daniel, We had some similar responses. I like your example of spherical coordinates for the location of a specific crater or mountaim on a different planet. Pretty cool to be able to find location on objects that are outside the limits of earth. I was thinking aircraft control for polar coordinates, but also found out they use a slightly modified version of the polar coordinates. Not sure exactly how it is slightly modified, but it definatley was the first thing that came to my mind as well. Finding the volume of a gas holder by using a cylindrical coordinates is a great example too. Thanks for sharing! (http Thomas Brown (https://sdccd.instructure.com/courses/2417891/users/8908701) Saturday Daniel, I hope that you had a good break and were able to relax a little. I know that I was not able to, had a lot to do over the break I really like your post. You truly have a very good understanding of the coordinate systems and that reflected in your post. I really enjoyed your reasoning on why we use different coordinate systems and I agree completely. It was different from my post since you focused on distance from a point while I looked at it as applying different equations to a coordinate system. In the end, it all is the same, your explanation was easier to understand so thank you. I enjoyed all of your definitions and uses for all of these different coordinate systems. For example, in your spherical coordinate definition, I really like how you stated that the realworld use of locating a large terrain feature. In your rectangular coordinate definition, I like how you simply stated all the planes that the system could be used in. This was really great work and I agree with everything that you said, Daniel. Thank you for your post, and have a great week. R/ Tom (http Qiyao You (https://sdccd.instructure.com/courses/2417891/users/8711375) Sunday Hi Daniel, I hope you had a great spring break! I really like your response because the definitions and examples you provided for each type of coordinates are very concise and easier to understand. I also have some similar answers to you, and I totally agree with you. I really https://sdccd.instructure.com/courses/2417891/discussion_topics/14550642?module_item_id=41176631 9/25 2021/4/6 Topic: Discussion Week 9 like your explanation of polar coordinates, and I am interested in polar coordinates out of all these four types of coordinates because it seems can apply a lot in our daily life. Regarding my rese…

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