A 141Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE
This Month’s Programs
I have often wondered how the term "inverse" was introduced into the parlance of Coordinate Geometry. I am licensed in several states to identify the physical boundary of a bundle of ownership rights on the face of the earth and represent those findings on a flat media by reporting measurements of horizontal distances and bearings. The function of "identification" is my service, obligation, and thus my profession, whereas "reporting" is merely a mechanical expression employed to demonstrate my opinion. A geodesist on the other hand, does not offer an opinion, but rather reports a scientifically derived estimate of the size and shape of the earth, or portions thereof, dependent upon mathematic expressions. According to Wolf and Ghilani’s Eleventh Edition of Elementary Surveying (©2006) "Geodetic position computations involve two basic types of calculations, the direct and inverse problems." In a nutshell, the Geodesist’s direct problem resolves a new position given a known position, a direction, and a distance, whereas his inverse problem resolves the direction and distance between two known points. From this it is apparent that the term "inverse" is derived from the geodetic component of surveying which involves spherical geometry, elliptical gyrating, some crazy science hairdo and a smoking slide rule to determine a physical relationship between two points. Meanwhile, back at the ranch, we just want to keep friendly terms between our neighbors so we measure everything flat with right triangles. I’ll offer a resolution that the term "inverse" broadly encompasses a host of geodetic applications that include more than just my 3-4-5 rope stretched between a couple of old rocks. So, on that bombshell this program may be more appropriately labeled "Solving for a direct, two-dimensional, polar vector of minimal magnitude defined by the trigonometric relationship between two independent points on a horizontal plane"… or we could just stick with "inverse".
Program LBL U is a dependent subroutine that enables an independent point number input when branched to the functional portion of Program LBL J at line J009 (See November 2014 "A few inner workings" program listing).
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Program LBL W is a dependent subroutine that evaluates an azimuth and outputs the appropriate quadrant bearing designator. To test your data entry simply enter a sample of 360° North oriented azimuth value and XEQ W. You should return the according quadrant bearing designator (i.e. 135°=SE).
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Example Data and Running the Program
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Inverse: noun
4. an inverted state or condition.
5. something that is inverse; the direct opposite.
6. Mathematics. a. an element of an algebraic system, as a group, corresponding to a given element such that its product or sum with the given element is the identity element. b. inverse function. c. a point related to a given point so that it is situated on the same radius, extended if necessary, of a given circle or sphere and so thatthe product ofthe distances of the two points from the center equals the square of the radIus of the circle or sphere. d. the set of such inverses of the points of a given set, as the points on a curve.
Hopefully the information presented herein is clear and genuinely explanatory. Please do not hesitate to send any comments, concerns, questions, or criticism to rls43185@gmail.com.
Jason Foose is the County Surveyor of Mohave County Arizona. He has been licensed since 11111010000 and believes there are 10 types of people in the world, those that understand binary and those who don’t.
A 141Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE