The atan2 function returns the angle between the positive x-axis and the point (x,y) in a plane, taking into account the signs of x and y to determine the correct quadrant. It is useful in applications involving vectors and rotations. Unlike the single-argument arctangent function, atan2 can distinguish between diametrically opposite angles and handles cases where x is zero.
Pipe insulation efficiency study unit |HEAT TRANSFER LaboratorySaif al-din ali
SAIF ALDIN ALI MADIN
سيف الدين علي ماضي
S96aif@gmail.com
1. Experiment Name: Pipe Insulation Efficiency Study Unit
2. Experiment Aim: The study unit for the assessment of thermal
insulation efficiency permits investigating the effect of thermal
insulation of steam pipes, the unit consist of a set of four pipes, three of
which are covered with insulating materials, placed vertically. Steam is
fed by means of an overhead manifold
3. Composition:
The lagging of piping unit includes:
1. - 3 test pipes covered with materials which thermal conductivity
coefficient is different.
2. One pipe without covering,
3. Manual control valve on steam inlet,
4. Bourdon pressure gauge on steam inlet
5. Thermometer in steam inlet
6. Condenser discharge system,
7. Graduated containers of glass to measure the condensate,
Complemento Teórico de la Guía de Trabajos Prácticos. El presente trabajo es un sumario de conceptos teóricos de la materia Estabilidad IIb (64.12) correspondiente a las carreras de Ingeniería Mecánica e Ingeniería Naval y Mecánica.
Free heat convection |HEAT TRANSFER LaboratorySaif al-din ali
SAIF ALDIN ALI MADIN
سيف الدين علي ماضي
S96aif@gmail.com
Experiment Name: Free Heat Convection from a Horizontal Heated
Cylinder
2. Experiment Aim:
1. Calculating the free heat convection coefficient (ℎ푁퐶) for a
horizontal heated solid cylinder.
2. Find the relationship between RaNo. And NuNo. for fluid flow
around a cylinder
Pipe insulation efficiency study unit |HEAT TRANSFER LaboratorySaif al-din ali
SAIF ALDIN ALI MADIN
سيف الدين علي ماضي
S96aif@gmail.com
1. Experiment Name: Pipe Insulation Efficiency Study Unit
2. Experiment Aim: The study unit for the assessment of thermal
insulation efficiency permits investigating the effect of thermal
insulation of steam pipes, the unit consist of a set of four pipes, three of
which are covered with insulating materials, placed vertically. Steam is
fed by means of an overhead manifold
3. Composition:
The lagging of piping unit includes:
1. - 3 test pipes covered with materials which thermal conductivity
coefficient is different.
2. One pipe without covering,
3. Manual control valve on steam inlet,
4. Bourdon pressure gauge on steam inlet
5. Thermometer in steam inlet
6. Condenser discharge system,
7. Graduated containers of glass to measure the condensate,
Complemento Teórico de la Guía de Trabajos Prácticos. El presente trabajo es un sumario de conceptos teóricos de la materia Estabilidad IIb (64.12) correspondiente a las carreras de Ingeniería Mecánica e Ingeniería Naval y Mecánica.
Free heat convection |HEAT TRANSFER LaboratorySaif al-din ali
SAIF ALDIN ALI MADIN
سيف الدين علي ماضي
S96aif@gmail.com
Experiment Name: Free Heat Convection from a Horizontal Heated
Cylinder
2. Experiment Aim:
1. Calculating the free heat convection coefficient (ℎ푁퐶) for a
horizontal heated solid cylinder.
2. Find the relationship between RaNo. And NuNo. for fluid flow
around a cylinder
SAIF ALDIN ALI MADIN
سيف الدين علي ماضي
S96aif@gmail.com
After insulating limited distance between jet hole and main
channel and find:
1. The static pressure distribution the along channel.
2. The velocity distribution on the section different dimensions.
3. The secondary flow rate discharge
4. The friction force F
Dear Sir/Mam,
I am Prasad Nimbalkar B.E.Mechanical fresher from VTU University Belgaum also having Diploma in Automobile. I am looking out for a career opportunity at Pune
I have attached my resume along this mail please go through it.
Hope you will find me suitable and reply soon.
Thanking you .
With Regards,
Prasad R. Nimbalkar.
IDC interviewed nine organizations that are using Red Hat OpenShift as their primary application development platform. These organizations reported that OpenShift helps them deliver timely and compelling applications and features across their complex and heterogeneous IT environments and supports key IT initiatives such as containerization, microservices, and cloud migration strategies.
SAIF ALDIN ALI MADIN
سيف الدين علي ماضي
S96aif@gmail.com
After insulating limited distance between jet hole and main
channel and find:
1. The static pressure distribution the along channel.
2. The velocity distribution on the section different dimensions.
3. The secondary flow rate discharge
4. The friction force F
Dear Sir/Mam,
I am Prasad Nimbalkar B.E.Mechanical fresher from VTU University Belgaum also having Diploma in Automobile. I am looking out for a career opportunity at Pune
I have attached my resume along this mail please go through it.
Hope you will find me suitable and reply soon.
Thanking you .
With Regards,
Prasad R. Nimbalkar.
IDC interviewed nine organizations that are using Red Hat OpenShift as their primary application development platform. These organizations reported that OpenShift helps them deliver timely and compelling applications and features across their complex and heterogeneous IT environments and supports key IT initiatives such as containerization, microservices, and cloud migration strategies.
IDC interviewed nine organizations that are using Red Hat OpenShift as their primary
application development platform. These organizations reported that OpenShift helps
them deliver timely and compelling applications and features across their complex and
heterogeneous IT environments and supports key IT initiatives such as containerization,
microservices, and cloud migration strategies.
I am Martina J. I am a Signals and Systems Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, from the University of Maryland. I have been helping students with their assignments for the past 9 years. I solve assignments related to Signals and Systems.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Signals and Systems assignments.
This presentation is a part of Computer Oriented Numerical Method . Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques.
I am Ronald N. I am a Numerical Analysis Assignment Solver at mathhomeworksolver.com. I hold a Master's in Mathematics, from Quebec, Canada. I have been helping students with their assignments for the past 10 years. I solved assignments related to Numerical Analysis.
Visit mathhomeworksolver.com or email support@mathhomeworksolver.com. You can also call on +1 678 648 4277 for any assistance with Numerical Analysis Assignment.
I am Katie P. I am a Maths Assignment Expert at mathsassignmenthelp.com. I hold a Master's in Mathematics from Concordia University. I have been helping students with their assignments for the past 10 years. I solve assignments related to Maths.
Visit mathsassignmenthelp.com or email info@mathsassignmenthelp.com.
You can also call +1 678 648 4277 for any assistance with Maths Assignments.
Contents of the presentation:
- ABOUT ME
- Bisection Method using C#
- False Position Method using C#
- Gauss Seidel Method using MATLAB
- Secant Mod Method using MATLAB
- Report on Numerical Errors
- Optimization using Golden-Section Algorithm with Application on MATLAB
Here are my slides in some basic algorithms in Computational Geometry:
1.- Line Intersection
2.- Sweeping Line
3.- Convex Hull
They are the classic one, but there is still a lot for anybody wanting to get in computer graphics to study. I recomend
Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars. 2008. Computational Geometry: Algorithms and Applications (3rd ed. ed.). TELOS, Santa Clara, CA, USA.
This paper introduces a new comparison base stable sorting algorithm, named RA sort. The RA sort
involves only the comparison of pair of elements in an array which ultimately sorts the array and does not
involve the comparison of each element with every other element. It tries to build upon the relationship
established between the elements in each pass. Instead of going for a blind comparison we prefer a
selective comparison to get an efficient method. Sorting is a fundamental operation in computer science.
This algorithm is analysed both theoretically and empirically to get a robust average case result. We have
performed its Empirical analysis and compared its performance with the well-known quick sort for various
input types. Although the theoretical worst case complexity of RA sort is Yworst(n) = O(n√), the
experimental results suggest an empirical Oemp(nlgn)1.333 time complexity for typical input instances, where
the parameter n characterizes the input size. The theoretical complexity is given for comparison operation.
We emphasize that the theoretical complexity is operation specific whereas the empirical one represents the
overall algorithmic complexity.
AN EFFICIENT LINE CLIPPING ALGORITHM FOR CIRCULAR WINDOWS USING VECTOR CALCUL...ijcga
With the advent of digitization and growing abundance of graphic and image processing tools, use cases
for clipping using circular windows have grown considerably. This paper presents an efficient clipping
algorithm for line segments using geometrical features of circle and vector calculus. Building upon the
research with rectangular windows, this method is proposed with the belief that computations are more
expensive (heavy) than other computations. Execution time can be drastically improved if we replace
expensive computations with cheaper computations. The cheaper computations can be computed even more
efficiently using parallelization thus improving time complexity.
An Efficient Line Clipping Algorithm for Circular Windows Using Vector Calcul...ijcga
With the advent of digitization and growing abundance of graphic and image processing tools, use cases for clipping using circular windows have grown considerably. This paper presents an efficient clipping algorithm for line segments using geometrical features of circle and vector calculus. Building upon the research with rectangular windows, this method is proposed with the belief that computations are more expensive (heavy) than other computations. Execution time can be drastically improved if we replace expensive computations with cheaper computations. The cheaper computations can be computed even more efficiently using parallelization thus improving time complexity.
AN EFFICIENT LINE CLIPPING ALGORITHM FOR CIRCULAR WINDOWS USING VECTOR CALCUL...ijcga
With the advent of digitization and growing abundance of graphic and image processing tools, use cases
for clipping using circular windows have grown considerably. This paper presents an efficient clipping
algorithm for line segments using geometrical features of circle and vector calculus. Building upon the
research with rectangular windows, this method is proposed with the belief that computations are more
expensive (heavy) than other computations. Execution time can be drastically improved if we replace
expensive computations with cheaper computations. The cheaper computations can be computed even more
efficiently using parallelization thus improving time complexity.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
1. Atan2 1
Atan2
In a variety of computer languages, the function atan2 is the arctangent function with two arguments. The purpose
of using two arguments instead of one, is to gather information of the signs of the inputs in order to return the
appropriate quadrant of the computed angle, which is not possible for the single-argument arctangent function.
For any real number (e.g., floating point) arguments x and y not both equal to zero, atan2(y, x) is the angle in radians
between the positive x-axis of a plane and the point given by the coordinates (x, y) on it. The angle is positive for
counter-clockwise angles (upper half-plane, y > 0), and negative for clockwise angles (lower half-plane, y < 0).
The atan2 function was first introduced in computer programming languages, but now it is also common in other
fields of science and engineering. It dates back at least as far as the FORTRAN programming language
[1]
and is
currently found in C's math.h standard library, the Java Math library, .NET's System.Math (usable from C#,
VB.NET, etc.), the Python math module, the Ruby Math module, and elsewhere. Many scripting languages, such as
Perl, include the C-style atan2 function.
[2]
In mathematical terms, atan2 computes the principal value of the argument function applied to the complex number
x+iy. That is, atan2(y, x) = Pr arg(x+iy) = Arg(x+iy). The argument can be changed by 2π (corresponding to a
complete turn around the origin) without making any difference to the angle, but to define atan2 uniquely one uses
the principal value in the range (−π, π]. That is, −π < atan2(y, x) ≤ π.
The atan2 function is useful in many applications involving vectors in Euclidean space, such as finding the direction
from one point to another. A principal use is in computer graphics rotations, for converting rotation matrix
representations into Euler angles.
In some computer programming languages, the order of the parameters is reversed (for example, in some
spreadsheets) or a different name is used for the function (for example, Mathematica uses ArcTan[x,y]). On
scientific calculators the function can often be calculated as the angle given when (x, y) is converted from rectangular
coordinates to polar coordinates.
Motivation
The one-argument arctangent function can not distinguish between diametrically opposite directions. For example,
the anticlockwise angle from the x-axis to the vector (1, 1), calculated in the usual way as arctan(1/1), is π/4
(radians), or 45°. However, the angle between the x-axis and the vector (−1, −1) appears, by the same method, to be
arctan(−1/−1), again π/4, even though the answer clearly should be −3π/4, or −135°.
The atan2 function takes into account the signs of both vector components, and places the angle in the correct
quadrant. Thus, atan2(1, 1) = π/4 and atan2(−1, −1) = −3π/4.
Additionally, the ordinary arctangent method breaks down when required to produce an angle of ±π/2 (or ±90°). For
example, an attempt to find the angle between the x-axis and the vector (0, 1) requires evaluation of arctan(1/0),
which fails on division by zero. In contrast, atan2(1, 0) gives the correct answer of π/2.
When calculations are performed manually, the necessary quadrant corrections and exception handling can be done
by inspection, but in computer programs it is extremely useful to have a single function that always gives an
unambiguous correct result.
2. Atan2 2
Definition and computation
In terms of the standard arctan function, whose range is (−π/2, π/2), it can be expressed as follows:
Notes:
• This produces results in the range (−π, π], which can be mapped to [0, 2π) by adding 2π to negative results.
•• Traditionally, atan2(0, 0) is undefined.
• The C function atan2, and most other computer implementations, are designed to reduce the effort of
transforming cartesian to polar coordinates and so always define atan2(0, 0). On implementations without
signed zero, or when given positive zero arguments, it is normally defined as 0. It will always return a value in
the range [−π, π] rather than raising an error or returning a NaN (Not a Number).
• Systems supporting symbolic mathematics normally return an undefined value for atan2(0,0) or
otherwise signal that an abnormal condition has arisen.
• For systems implementing signed zero, infinities, or Not a Number (for example, IEEE floating point), it is
common to implement reasonable extensions which may extend the range of values produced to include −π and
−0. These also may return NaN or raise an exception when given a NaN argument.
• For systems implementing signed zero (for example, IEEE floating point), atan2(-0, x), x < 0 returns the value
−π. atan2(+0, x), x < 0 still returns +π.
The free math library FDLIBM (Freely Distributable LIBM) available from netlib has source code showing how it
implements atan2 including handling the various IEEE exceptional values.
For systems without a hardware multiplier the function atan2 can be implemented in a numerically reliable
manner by the CORDIC method. Thus implementations of atan(y) will probably choose to compute
atan2(y,1).
The following expression derived from the tangent half-angle formula can also be used to define atan2.
This expression may be more suited for symbolic use than the definition above. However it is unsuitable for floating
point computational use as it is undefined for y = 0, x < 0 and may overflow near these regions. The formula gives an
NaN or raises an error for atan2(0, 0), but this is not an issue since atan2(0, 0) is not defined.
A variant of the last formula is sometimes used in high precision computation. This avoids overflow but is always
undefined when y = 0:
3. Atan2 3
Variations and notation
• In Common Lisp, where optional arguments exist, the atan function allows one to optionally supply the x
coordinate: (atan y x).
[3]
• In Mathematica, the form ArcTan[x, y] is used where the one parameter form supplies the normal
arctangent. Mathematica classifies ArcTan[0, 0] as an indeterminate expression.
• In Microsoft Excel, the atan2 function has the two arguments reversed.
[4]
OpenOffice.org Calc also reverses
the arguments, as does the Google Spreadsheets <atan2 function.
[5]
• In the Intel Architecture assembler code, atan2 is known as the FPATAN (floating-point partial arctangent)
instruction.
[6]
It can deal with infinities and results lie in the closed interval [−π, π], e.g. atan2(∞, x) = +π.
Particularly, FPATAN is defined when both arguments are zero:
atan2(+0, +0) = +0
atan2(+0, −0) = +π
atan2(−0, +0) = −0
atan2(−0, −0) = −π
This definition is related to the concept of signed zero, i.e.
• On most TI graphing calculators (excluding the TI-85 and TI-86), the equivalent function is called R►Pθ and has
the arguments reversed.
• In mathematical writings other than source code, such as in books and articles, the notations Arctan
[7]
and
Tan
-1[8]
have been utilized; these are uppercase variants of the regular arctan and tan
-1
. This usage is consistent
with the complex argument notation, such that Atan(y, x) = Arg(x+iy).
4. Atan2 4
Illustrations
atan2 round a circle
The diagram alongside shows values of
atan2 at selected points on the unit
circle. The values, in radians, are
shown inside the circle. The diagram
uses the standard mathematical
convention that angles increase
anticlockwise (counterclockwise), and
zero is to the right. Note that the order
of arguments is reversed; the function
atan2(y, x) computes the angle
corresponding to the point (x, y).
The diagram below shows values of
atan2 for points on the unit circle. On
the x-axis is the complex angle of the
points, starting from 0 ( point (1,0) )
and going anticlockwise
(counterclockwise), through points:
•• (0, 1) with complex angle π/2 (in
radians),
• (−1, 0) with complex angle π,
• (0, −1) with complex angle 3π/2,
to (1, 0) with complex angle 0 = (2nπ
mod 2π).
On this diagram one can clearly see the discontinuity of the atan2 function.
[9]
The diagrams below show 3D view of respectively atan2(y, x) and arctan(y/x) over a region of the plane.
Note that for atan2, rays emanating from the origin have constant values, but for atan lines passing through the origin
have constant values. For x > 0, the two diagrams give identical values.
5. Atan2 5
Derivative
As the function atan2 is a function of two variables, it has two partial derivatives. At points where these derivatives
exist, atan2 is, except for a constant, equal to arctan(y/x). hence:
for
Informally representing the function atan2 as the angle function (which is only defined up
to a constant) yields the following formula for the total derivative:
While the function atan2 is discontinuous along the negative y-axis, reflecting the fact that angle cannot be
continuously defined, this derivative is continuously defined except at the origin, reflecting the fact that infinitesimal
(and indeed local) changes in angle can be defined everywhere except the origin. Integrating this derivative along a
path gives the total change in angle over the path, and integrating over a closed loop gives the winding number.
In the language of differential geometry, this derivative is a one-form, and it is closed (its derivative is zero) but not
exact (it is not the derivative of a 0-form, i.e., a function), and in fact it generates the first de Rham cohomology of
the punctured plane. This is the most basic example of such a form, and it is fundamental in differential geometry.
The partial derivatives of atan2 do not contain trigonometric functions, making it particularly useful in many
applications (e.g. embedded systems) where trigonometric functions can be expensive to evaluate.Wikipedia:Please
clarify
6. Atan2 6
References
[2] The Linux Programmer's Manual (http://linux.die.net/man/3/atan2) says:
"The atan2() function calculates the arc tangent of the two variables y and x. It is similar to calculating the arc
tangent of y / x, except that the signs of both arguments are used to determine the quadrant of the result."
[6] IA-32 Intel Architecture Software Developer’s Manual. Volume 2A: Instruction Set Reference, A-M, 2004.
[7] http://books.google.com/books?id=2LIMMD9FVXkC&pg=PA234&dq=four+quadrant+inverse+tangent+mathematical+notation&
hl=en&sa=X&ei=Q2Y4UaGTAcmzyAHsooCoBw&ved=0CDgQ6AEwAg#v=onepage&
q=four%20quadrant%20inverse%20tangent%20mathematical%20notation&f=false
[8] http://books.google.com/books?id=7nNjaH9B0_0C&pg=PA345&dq=four+quadrant+inverse+tangent+mathematical+notation&
hl=en&sa=X&ei=Q2Y4UaGTAcmzyAHsooCoBw&ved=0CDIQ6AEwAQ#v=onepage&
q=four%20quadrant%20inverse%20tangent%20mathematical%20notation&f=false
[9] Computation of the external argument by Wolf Jung (http://www.mndynamics.com/indexp.html)
External links
• Java 1.6 SE JavaDoc (http://java.sun.com/javase/6/docs/api/java/lang/Math.html#atan2(double, double))
• atan2 (http://everything2.com/index.pl?node_id=1008481) at Everything2
• PicBasic Pro solution (http://www.picbasic.co.uk/forum/showthread.php?p=70269#post70269) atan2 for a
PIC18F
Other implementations/code for atan2
• Bearing Between Two Points (http://mathforum.org/library/drmath/view/55417.html)
• Arctan and Polar Coordinates (http://mathforum.org/library/drmath/view/54114.html)
• What's 'Arccos'? (http://mathforum.org/library/drmath/view/54172.html)