Mapping Math: Introduction - Revision history

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Wiki-Sunburned Surveyor at 19:44, 24 July 2009

2009-07-24T19:44:06Z

Wiki-Sunburned Surveyor: /* Why is Mapping Math needed? */

2009-07-24T19:43:05Z

Why is Mapping Math needed?

Wiki-Sunburned Surveyor: /* What are the goals of Mapping Math? */

2009-07-24T19:42:48Z

What are the goals of Mapping Math?

Wiki-Sunburned Surveyor: /* What are the goals of Mapping Math? */

2009-07-24T19:42:36Z

What are the goals of Mapping Math?

Wiki-Sunburned Surveyor at 19:42, 24 July 2009

2009-07-24T19:42:08Z

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Wiki-Sunburned Surveyor at 16:16, 28 December 2006

2006-12-28T16:16:09Z

@@ Line 74: / Line 74: @@
 [http://wiki.osgeo.org/wiki/Mapping_Math Mapping Math Home]
-[[Categories: Education]]
+[[Category: Education]]
-[[Categories: Mapping Math]]
+[[Category: Mapping Math]]

@@ Line 72: / Line 72: @@
 ==Navigation==
-[[Mapping Math Home]]
+[http://wiki.osgeo.org/wiki/Mapping_Math Mapping Math Home]
 [[Categories: Education]]
 [[Categories: Mapping Math]]

← Older revision		Revision as of 19:44, 24 July 2009
Line 70:		Line 70:

	If you find a mistake, please send an e-mail to sunburned.surveyor@gmail.com and let me know about it. I'll get it fixed as soon as I can. While we are on the subject, let me also add that you are welcome to send me suggestions and ideas for the book. Also do not hesitate if you want to help me with the writing of the book, or with translation into a language other than English.		If you find a mistake, please send an e-mail to sunburned.surveyor@gmail.com and let me know about it. I'll get it fixed as soon as I can. While we are on the subject, let me also add that you are welcome to send me suggestions and ideas for the book. Also do not hesitate if you want to help me with the writing of the book, or with translation into a language other than English.
		+
		+	==Navigation==
		+	[[Mapping Math Home]]
		+
		+	[[Categories: Education]]
		+	[[Categories: Mapping Math]]

← Older revision		Revision as of 19:43, 24 July 2009
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−	'''Math is not the enemy. The enemy is those that think math should be easy for all to grasp and understand.'''	+	'''Math is not the enemy. The enemy is those that think math should be easy for all to grasp and understand.'''
−

	==Author Bias==		==Author Bias==

← Older revision		Revision as of 19:42, 24 July 2009
Line 8:		Line 8:

	I have the following goals for this series of articles:		I have the following goals for this series of articles:
−

	*Collect together in a single place the mathematical concepts needed by land surveyors and geospatial professionals.		*Collect together in a single place the mathematical concepts needed by land surveyors and geospatial professionals.

@@ Line 10: / Line 10: @@
-Collect together in a single place the mathematical concepts needed by land surveyors and geospatial professionals.
+*Collect together in a single place the mathematical concepts needed by land surveyors and geospatial professionals.
-Teach these concepts in an informal style and easy-to-understand manner.
+*Teach these concepts in an informal style and easy-to-understand manner.
-Release this content under an “open” license that allows it to be freely copied, distributed, and translated into other languages.
+*Release this content under an “open” license that allows it to be freely copied, distributed, and translated into other languages.
-Make basic computer programming in a modern programming language (and the application of computer programming to math problems) a central part of the articles.
+*Make basic computer programming in a modern programming language (and the application of computer programming to math problems) a central part of the articles.
 ==Background==

← Older revision	Revision as of 19:42, 24 July 2009
Line 1:	Line 1:
	+	=Mapping Math: Introduction=

	+	==What is Mapping Math?==
	+
	+	Mapping Math is a series of articles I hope to write as part of my work with the OSGeo Education Committee. The articles will teach the mathematical concepts used by land surveyors and other geospatial professionals. Each article will discuss a single topic on this greater subject. All of the articles will follow the same basic template.
	+
	+	==What are the goals of Mapping Math?==
	+
	+	I have the following goals for this series of articles:
	+
	+
	+	Collect together in a single place the mathematical concepts needed by land surveyors and geospatial professionals.
	+	Teach these concepts in an informal style and easy-to-understand manner.
	+	Release this content under an “open” license that allows it to be freely copied, distributed, and translated into other languages.
	+	Make basic computer programming in a modern programming language (and the application of computer programming to math problems) a central part of the articles.
	+
	+	==Background==
	+
	+	This series of articles started out as the idea for a book. After the “book” had suffered from a lack of my attention for many months, I decided it might be more successful if I wrote the material as a series of related, but independent articles. I discussed this idea with Charlie Schweik, the chairman of the OSGeo Education Committee, and he seemed open to letting me explore it. I believe writing the material for Mapping Math as a series of articles instead of a book will accomplish several things:
	+
	+	*It will make the task seem less overwhelming.
	+	*It will allow me to actually accomplish something, even if “something” comes in small packages.
	+	*It will make it easier for other authors to contribute.
	+
	+	==Why is Mapping Math needed?==
	+
	+	I have found that there is a big difference between the type of people that understand math, and the type of people that can teach math in a way that is easily understood by others. It seems like there are a lot more of the first type of people than there are the second type. This presents a serious problem for some students of mathematics.
	+
	+
	+	I struggled with math growing up. I know this was partly due to my own lack of ability, but I think it was also due to math teachers that had little sympathy for students to whom math did not just “make sense”. My introduction to algebra as a young teenager was a surprise, because it was the first type of math I had encountered that I didn't despise. Even so, I struggled with algebra as I had all the other types of math before it. I would consistently score lower in math than in any other subject on standardized tests.
	+	I am telling you as the reader this small part of my own history because I want you to know that I understand what it is like to fight math and loose the brawl. I am finally winning this fight in my own life, and I now use math every single day. In my own life Math has been transformed from a frustrating obstacle to a powerful tool. I hope this background will help me to be a better math teacher, and will make it easier for you to benefit from this series of articles.
	+
	+
	+	I wanted to write some instructions on the math used in mapping that could be understood by all types of people, even by those who found math difficult. I personally think that traditional math books are horrible creatures that should be forever banned from the classroom. (My two favorite math books are “Idiot's Guide to Calculus” and “Calculus for Dummies.) I have also found that there is not a great deal of material available about the math used by mapping professionals, and certainly none as freely available as I hope the content of this book will be. (The book “The 3-D Global Spatial Data Model” is the first thing I have seen that comes close to providing a collection of the math needed by mappers.) This frustration has been shared with me by other surveyors and geospatial professionals. I hope this will fill what I see as a serious void in the material on math for the professional that works with spatial data or maps, whether that is a Land Surveyor or GIS Professional.
	+
	+
	+	I found that I really enjoyed math and its ability to solve problems when I could see how it was practically applied in land surveying. That transition from “purely conceptual math” to math in its role as a practical tool made a big difference for me as a math student. I want to show others how math concepts are applied to the making of maps and spatial data. Perhaps others will come to love math as I have when they see how math can be used as a tool in their own work. In the Mapping Math series of articles I hope to avoid the abstract as much as possible and focus on the practical whenever possible.
	+
	+
	+	'''Math is not the enemy. The enemy is those that think math should be easy for all to grasp and understand.'''
	+
	+
	+	==Author Bias==
	+	All authors taint their written works with a bias or slant that is as unique as they are unique as individuals. I am no exception to this rule. I want to provide you with a little bit of information about myself, so that you can recognize and understand my bias when you read this series of articles. I'm sure this bias will creep in despite by efforts to remain objective. This will also help the reader understand why some other mapping professionals may disagree with my style or portions of the material, and be justified in doing so.
	+
	+
	+	First of all, the reader should understand that my day job is as a Land Surveyor. As I mentioned earlier, I use math in my work every day, and in my world trigonometry rules as King. I deal mostly with the making and analyzing measurements, and with the act of creating spatial data. As a result some of the material in this book may focus on the math used in those processes. Land Surveyors also tend to be a little more particular about the accuracy and precision of spatial data than other mapping professionals, and this may be evident in this book occasionally.
	+
	+
	+	Secondly, I should let you know that most of my experience with GIS is as a programmer or software developer. (Although I have embarked on a couple of projects that I hope will help to remedy this.) This means my expertise in the math behind spatial analysis will be a little weaker. (What a great opportunity this would be for a fellow mapping professional with a noble heart to step in as a contributing author.) I still understand the concepts of this area of GIS and I hope to discuss it in some sections of the book.
	+
	+
	+	Finally, I must tell you that I'm not a highly educated man by the standards of “modern society”, for lack of a better term. I learned about land surveying and GIS at my community college in Montana, but did not have any “higher” education after that. All of my other knowledge has been gained through practical experience on the job or by self instruction and volunteer projects. I personally think that “higher” education can be overrated, and that practical experience and self instruction can be just as, or more, beneficial. At any rate, I have no fancy degrees, diplomas, certifications, or titles, and I don't have any letters that follow my name. I thought I would warn those among my readers who feel that is important.
	+
	+	==Who is this series of articles written for?==
	+
	+	Although I hope it appeals to all kinds of people, I am targeting two (2) types of people specifically with this book. The first type of person is new to process of map making and digital maps. The second type of person may have some experience in one of these areas, but would like to tackle more of the math behind the work they do. For everyone else, this material will hopefully serve as a good review.
	+
	+	==Style and Format==
	+
	+	The style of this series of articles will be very informal. I've already mentioned how I feel about stuffy and mechanical math text books, and I definitely won't be writing a articles that would be approved of by one of those publishers. I'm going to go out of my way to do the following in each article:
	+
	+	# Show every single step when solving a math problem.
	+	# Clearly define and explain unfamiliar terms.
	+	# Clearly indicate and highlight important terms and formulas.
	+	# Explain the concept and practical application of the math, not just have you memorize rules and formulas.
	+	# Use lots of diagrams and pictures.
	+
	+	The informal style I hope to use does not mean that I want to have mistakes or errors. I want each article to be as grammatically and technically correct as possible. I also don't want any math mistakes. (Yes, I do make math mistakes and I have seen them in math books.)
	+
	+	==How can you help?==
	+
	+	If you find a mistake, please send an e-mail to sunburned.surveyor@gmail.com and let me know about it. I'll get it fixed as soon as I can. While we are on the subject, let me also add that you are welcome to send me suggestions and ideas for the book. Also do not hesitate if you want to help me with the writing of the book, or with translation into a language other than English.

← Older revision		Revision as of 14:28, 28 October 2007
Line 1:		Line 1:
−	~~==What is this chapter about?==~~
−	This chapter of the Free GIS Book explains some of the math that is encountered when you work with digital maps, hard copy or paper maps, and other types of spatial data. In this chapter you will learn about the measurements that are used to create spatial data. This includes the math used to make these measurements and to manipulate them. After this we will talk about triangles and basic trigonometry. This knowledge will be important when we learn about 2D, or two-dimensional, coordinate geometry. (Raw measurements are converted to coordinate geometry, a form of information that can be used by most mapping programs.) We will extend our discussion of coordinate geometry to include 3D, or three-dimensional, coordinate geometry. Then we will talk in detail about map scale and some of the math involved in the layout of hard copy maps. We will finish the chapter by looking at some of the math behind a simple map projection.

−	This chapter does not include instruction on all of the math you will need to work with maps and other types of spatial data. It is not a math book. It does not cover in detail basic arithmetic or algebra. It does provide comprehensive coverage of basic trigonometry and basic coordinate geometry, but it is not an exhaustive treatment of these subjects. I've left lots of room for improvement and additional material.
−
−	~~==What do you need to have before you read this chapter of the Free GIS Book?==~~
−	You need to have several things with you to benefit fully from this chapter of the Free GIS Book. You'll need a pencil and some paper. You'll also need a calculator that has the ability to calculate the trigonometric functions sin, cosine, and tangent. (I'll explain where to find these buttons on your calculator in the section of this chapter that deals with trigonometry.) Your calculator should also be able to compute square roots. You should have a knowledge of basic arithmetic and a knowledge of basic algebra. (This means you should be comfortable adding, subtracting, multiplying, dividing and solving simple equations.)
−
−	~~==Why am I writing this chapter of the Free GIS Book?==~~
−	Let me explain why I am taking the time to write this chapter of the Free GIS Book. I have personally found that there is a big difference between people that understand math, and people that can teach math in a way that is easily understood by others. It seems like there are more people in the first category than there are in the second. I struggled with math as a boy. This was partly due to my own abilities, but partly due to teachers that had little sympathy for those to whom math did not just “make sense”. My introduction to algebra as a young teenager was a surprise, because it was the first type of math I had encountered that I didn't despise. Even so, I struggled with algebra as I had all the other types of math before it. I would consistently score lower in math than in any other subject on standardized tests. I am telling you this because I want you to know that I understand what it is like to fight math and loose the brawl. I am finally winning this fight in my own life, and I now use math every single day. I hope this background will help me to be a better math teacher, and will make this a better chapter of the Free GIS Book.
−
−	I wanted to write some instructions on the math used in mapping that could be understood by all types of people, even by those who found math difficult. I personally think that traditional math books are horrible creatures that should be forever banned from the classroom. (My two favorite math books are “Idiot's Guide To Calculus” and “Calculus for Dummies.) I have also found that there is not a great deal of material available about the math used by mapping professionals, and certainly none as freely available as the content of the Free GIS Book. This frustration has been shared with me by other surveyors and Gis professionals. I hope this chapter will help to fill that void.
−
−	I found that I really enjoyed math and its ability to solve problems when I could see how it was practically applied in land surveying. That transition from purely concept to concept and application made a big difference for me as a math student. I want to show others how math concepts are applied to the making of maps and spatial data. Perhaps others will come to love math as I have when they see this.
−
−	~~==Who is writing this chapter of the Free GIS Book?==~~
−	All authors taint their written works with a bias or slant that is as unique as they are as individuals. I am no exception to this rule. I want to provide you with a little bit of information about myself, so that you can recognize and and understand my bias when you read this chapter of the Free GIS Book. I'm sure this bias will creep in despite by efforts to remain objective. This will also help the reader understand why some other mapping professionals may disagree with my style or protions of my material, and be justified in doing so.
−
−	First of all, the reader should understand that my day job is as a Land Surveyor. (I'm not a licensed land surveyor just yet. I'm still in training.) As I mentioned earlier, I use math in my work every day, and in my world trigonometry rules as King. I deal mostly with the making and analyzing measurements, and with the act of creating spatial data. As a result most of the material in this chapter focuses on the math used in those processes. Land Surveyors also tend to be a little more particular about the accuracy and precision of spatial data than other mapping professionals, and this may pickyness may be evident in this chapter occasionally.
−
−	Secondly, I should let you know that most of my experience with GIS is as a programmer or software developer. (Although I have embarked on a couple of projects that I hope will help to remedy this.) This means my expertize in the math behind spatial analysis will be a little weaker. (What a great opportunity this would be for a fellow mapping professional with a noble heart to step in as a contributing author of this chapter...) I still understand the concepts of this area of GIS and may be brave enough to talk about it in additional sections of the chapter. We'll have to see how things go.
−
−	Finally, I must tell you that I'm not a highly educated man by the standards of “modern society”, for lack of a better term. I learned about land surveying and GIS at my community college in Montana, but did not have any “higher” education after that. All of my other knowledge has been gained through practical experience on the job or by self instruction and volunteer projects. I personally think that “higher” education can be overrated, and that practical experience and self instruction can be just as, or more, beneficial. At any rate, I have no fancy degrees, diplomas, certifications, or titles, and I don't have any letters that follow my name. I thought I would warn those among my readers who feel that is important.
−
−	~~==What is my target audience?==~~
−	Although I hope it appeals to all kinds of people, I am targeting 2 types of people specifically with this chapter. The first type of person is new to land surveying, GIS, and mapping. The second type of person may have some experience in one of these professions, but would like to tackle more of the math behind the work they do. For everyone else, this material will hopefully serve as a good review.
−
−	I'd like to finish up with some words about the style and format of this chapter. There hasn't been a lot of material written for the Free GIS Book at this point in time, and I feel like a pioneer somewhat. I have an idea of what direction I want to head, but now definitive guide on how to get there.
−
−	The style of this chapter will be very informal. I've already mentioned how I feel about stuffy and mechanical math text books, and I definitely won't be writing a chapter that would be accepted by one of those publishers. I'm going to go out of my way to do the following in this chapter:
−
−	~~[1] Show every single step when solving a math problem.~~
−
−	~~[2] Clearly define and explain unfamiliar terms.~~
−
−	~~[3] Clearly indicate and highlight important terms and formulas.~~
−
−	~~[4] Explain the concept and practical application of the math, not just have you memorize rules and formulas.~~
−
−	~~[5] Use lots of diagrams and pictures.~~
−
−	The informal style I hope to use does not mean that I want to have mistakes or errors. I want this chapter to be as grammatically and technically correct as possible. I also don't want any math mistakes. (Yes, I do make math mistakes and I have seen them in other math books.)
−
−	~~==How can you help?==~~
−	If you find a mistake, please send an e-mail to sunburned.surveyor@gmail.com and let me know about it. I'll get it fixed as soon as I can. While we are on the subject, let me also add that you are welcome to send me suggestions and ideas for the chapter. Also do not hesitate if you want to help me with the writing of the chapter, or with translation into a language other than English.
−
−	~~----~~
−
−	~~==Navigation==~~
−
−	~~[http://wiki.osgeo.org/index.php/Mapping_Math Mapping Math Chapter Home]~~
−
−	~~[http://wiki.osgeo.org/index.php/Free_GIS_Book Free GIS Book Home]~~

← Older revision		Revision as of 16:17, 28 December 2006
Line 50:		Line 50:

	[http://wiki.osgeo.org/index.php/Mapping_Math Mapping Math Chapter Home]		[http://wiki.osgeo.org/index.php/Mapping_Math Mapping Math Chapter Home]
		+
		+	[http://wiki.osgeo.org/index.php/Free_GIS_Book Free GIS Book Home]

@@ Line 4: / Line 4: @@
 This chapter does not include instruction on all of the math you will need to work with maps and other types of spatial data. It is not a math book. It does not cover in detail basic arithmetic or algebra. It does provide comprehensive coverage of basic trigonometry and basic coordinate geometry, but it is not an exhaustive treatment of these subjects. I've left lots of room for improvement and additional material.
-==What do you need to have before you read this chapter of the Free GIs Book?==
+==What do you need to have before you read this chapter of the Free GIS Book?==
 You need to have several things with you to benefit fully from this chapter of the Free GIS Book. You'll need a pencil and some paper. You'll also need a calculator that has the ability to calculate the trigonometric functions sin, cosine, and tangent. (I'll explain where to find these buttons on your calculator in the section of this chapter that deals with trigonometry.)  Your calculator should also be able to compute square roots. You should have a knowledge of basic arithmetic and a knowledge of basic algebra. (This means you should be comfortable adding, subtracting, multiplying, dividing and solving simple equations.)