Spherical Zone with Manim

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Partial spherical zone

The sphere is of radius 4 units, it is hardcoded to the parametric equations. The parametric equations are as follows:

  • $x = r \cos \theta \sin \varphi$
  • $y = r \cos \theta \cos \varphi$
  • $z = r \cos \varphi$

If you check the code, you can see that the latitude and longitude of the sphere are reoriented. The reason is for the sphere to fit the Manim's camera settings.

The orientation of the camera was done by trial and error until I found a view that I wanted.

Files for Download are Now Available to $\require{cancel} \xcancel{\text{Non-}}$logged-in Users

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UPDATE: Starting May 2024, only logged-in users are allowed to download files.

MATHalino's philosophy, I may say, is that our contents must be accessible to all. Whether you are logged in or not, you can still access all our contents without any constraint. We already done this last year to our Courses and Exams, and this year we extend it to downloads.
 

pexels-miguel-a-padria-an-2882550.jpg

 

MATHalino Now Offers Online Courses

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This is not an announcement or promotional post. This is about my experience in building the platform for online courses.

 

Creating an online course is monumental specially to a small website like MATHalino. Despite being manned by one person from the ground up, the development of this functionality is actually progressing by degrees. I've been conceiving this feature as far as I can recall, way before online courses become a common thing in the Philippines. What makes me unable to implement it before comes from three factors.
 

Wazzup at MATHalino.com: July 2015

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For this year, we already serve about 5.5 million page views from about 800 thousand unique visitors, 40.2% of which are returning visitors spending an average of 6 minutes per visit. Thank you for the time you spent to us, your repeat visits showed that you made us a part of your growth in our subjects. We are about to reach 25 thousand likes in our FB page. We owe all of these from your trust to our contents and we are deeply grateful to that. Despite of no marketing arm and no single cent spent to promote the site, we reach this milestone all because of your trust to us. Thank you very much.

Polar Coordinate Printable Paper (Free Download)

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This is just a quick post and I hope you will find this useful.
 

Polar Coordinates

 

One time, I browse for something at the Morayta branch of National Book Store and I heard a group of students asking to the sales lady if they have a polar graph paper. From the look of her face, the sales lady seemed know nothing about a polar paper and she courteously told the students that they don't have what they are looking.
 

Calculator Technique for Solving Volume Flow Rate Problems in Calculus

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The following models of CASIO calculator may work with this method: fx-570ES, fx-570ES Plus, fx-115ES, fx-115ES Plus, fx-991ES, and fx-991ES Plus.
 

The following calculator keys will be used for the solution

Name Key Operation
Shift shift.jpg SHIFT
Mode mode-setup.jpg MODE
Name Key Operation
Stat 1-stat.jpg SHIFT → 1[STAT]
AC ac-off.jpg AC

 

This is one of the series of post in calculator techniques in solving problems. You maybe interested also on my previous post in calculator technique for progression problems and calculator technique for clock problems; both in Algebra.
 

Calculator Technique for Clock Problems in Algebra

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The following models of CASIO calculator may work with these methods: fx-570ES, fx-570ES Plus, fx-115ES, fx-115ES Plus, fx-991ES, and fx-991ES Plus.
 

Before we go to Calculator technique, let us first understand the movements of the hands of our continuously driven clock.
 

For simplicity, let "dial" be the unit of one hand movement and there are 60 dials in the complete circle as shown in the figure.
 

Calculator Techniques for Solving Progression Problems

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This is the first round for series of posts about optimizing the use of calculator in solving math problems. The calculator techniques I am presenting here has been known to many students who are about to take the engineering board exam. Using it will save you plenty of time and use that time in analyzing more complex problems. The following models of CASIO calculator may work with these methods: fx-570ES, fx-570ES Plus, fx-115ES, fx-115ES Plus, fx-991ES, and fx-991ES Plus.
 

Calculator for Engineering Board Exam

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Any one who took an engineering board examination will agree with me that scientific calculator is our best friend during the examination. It will speed up our work and will allow us to go through the analysis of the problem. In most cases, solving the equation is not the real issue, it is to write the correct equation that matters. If we are able to determine the correct equation of a particular situation, the burden of that problem is over. Our next step is obviously to solve for the desired value. It is important to note that the correct answer can only be derived from the correct equation. To determine the correct equation is where should our brain go, not in finding the solution of that equation. You guess it right, we use our best friend, the scientific calculator, to do the task. Don't do manual calculation please, the examiner will not give you bonus points in finding the roots of
 

$9\sin^{3/4} \theta + 4\sin^{3/2} \theta - 12 = 0$

 

manually. Calculator can easily solve for the value of θ fast and accurate than you.