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Montessori knobbed cylinders: the mathematics of radius, height, and volume

Volume of a Cylinder  The volume \(V\) of a cylinder with radius \(r\), height \(h\) is given by \[V = \pi r^2 h.\] Notice that we have three parameters. If we hold one of them to be constant, then we can obtain the relationship between the other two parameters, especially if one of these two parameters is uniformly or linearly increasing, i.e., a linear function of a set of integers \(k =\{0, 1, 2, \ldots, n\}\), where \(n\) is an arbitrary integer ideally greater than or equal to 3.  Let us consider three cases: constant volume, constant radius, and constant height. Each of these cases will have two sub-cases, with each sub-case dictating the design of a row of Montessori knobbed cylinders. Thus, in principle, you can design a total of 6 rows of knobbed cylinders, with each row containing \(n\) cylinders. 1. Constant volume \(V\) If the volume \(V=V_0\) is constant, then the radius \(r\) of the cylinder is inversely proportional to the square root of the height \(h\): \[r =\sqrt{\fra

How to download Optica's LaTeX template in Overleaf

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Fig. 1. Overleaf's user interface for the Optica journal template. The menu button is at the upper left corner.  Newsletter: Volume 1, Issue 1 (Feb 2023)  Topic: Research Contents: Optica's directions for downloading LaTeX files Overleaf's menu button for downloading source files My rendered LaTeX code using pdflatex in TeXworks I was using the free Overleaf account and one of its deal-breaking restrictions is the one-minute compile time. I can increase the compile time to 4 min if I get the Personal (USD 129), Standard (USD 199), and or Professional (  USD 399) Overleaf plan .  If your project has too many figures and style files, Overleaf would need more time to compile it, which can exceed the 1 minute mark.  One way to go around these restrictions is to compile your LaTeX code in your computer using the journal style files from Overleaf. Optica, for example, states that this manual compilation is possible: Choose the journal-specific "Access on Overleaf" link

Why marketing is like creating a religious cult around your brand

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Marketers peddle products that solve mankind's desire for comfort, health, and long life. That is why marketers sell air conditioning system during a hot summer, antibiotics when we get ill, and vitamin supplements for removing our wrinkles. But the greatest marketers are those who market an idea that solves mankind's greatest problem: death. One such marketer is Sauron. To Ar-Pharazon the King of the Numenorians who sensed his impending death, Sauron made his marketing spiel: The Valar have possessed themselves of the land where there is no death; and they lie to you concerning it, hiding it as best they may, because of their avarice, and their fear lest the Kings of Men should wrest from them the deathless realm and rule the world in their stead. And though, doubtless, the gift of life unending is not for all, but only for such as are worthy, being men of might and pride and great lineage, yet against all Justice is it done that this gift, which is his due, should be wit

Microscheduling at 10-minute resolution using a B5 notebook

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Microscheduling notebook According to the Business Dictionary , scheduling for a period of less than one day is called microscheduling. If you are scheduling a task to be done in the morning or evening, then you are microscheduling. If you you are scheduling your classes and meetings at intervals of 30 minutes or 1 hour, then you are microscheduling. But you may wish to push this further by microscheduling at 10 minute intervals, since short tasks normally last 10 minutes and a sequence of these small tasks can already finish a two-hour project. A. How to make a microscheduling table Divide the page of a 26-ring, B5-size binder notebook into half lengthwise using a red pen. Divide each page half into 6 parts with about 6 lines her hour. Draw horizontal red lines to separate the hours. The result is a 6x2 table per page, which looks like a collection of index cards. Using red ink, label 0 to 5 in the upper left hand corner of the left half, then 6 to 11 for those in the right hal

8 blogging personas based on Dungeons & Dragons characters

A blogging persona is a person you wish to project to your reader. Think of a persona as a  mask , because that is what it originally is. But a blogging persona is more malleable than a mask, because it acquires a certain personality. So you can think of a persona as character in a role-playing game like Dungeons and Dragons. By being consistent in your blogging persona, you define your blog's brand. Here are some examples: 1. Wizard  This blogger casts spells on his reader, such as the marketers's suggestion spells: "as you relax on your chair and drink your cappuccino, you wonder what it is like to live in a larger house for your growing family." He may also use magic wands, staves, socks, and shoes: "Buy our scientifically designed shoes and we guarantee that you'll run faster than before." 2. Fighter This blogger loves war with words.  He may be a street fighter who writes expletives before throwing those verbal punches and kicks.  He may als

One blog or many blogs, that is the question

I have been trying to answer these questions again and again. And my blogger friend would always laugh at me and say that she also had too many blogs before; now, she just have one blog. And she advises me to do likewise. Having many blogs has advantages. A blog with a different name gives you focus. It is as if you are donning a costume and do your specific superhero duties. And you become recognized by your blog's name. Then you don another costume and do another superhero duty. One day you are Superman--super strong, super fast, but super weak when faced with a Kryptonite. The next day you are Batman--intelligent, good-looking, martial arts expert, and billionaire. The costumes by themselves do not give Superman and Batman extraordinary powers; rather, the costumes provide a reminder of their identities as superheroes with specific functions and missions, in the same way as the habits of religious priests and nuns remind them of their chosen habits in life, i.e. how they

How to write a thesis proposal

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  Newsletter: Volume 1, Issue 1/ Topic: Research Contents Title Abstract Introduction Methodology Expected Results References  Budget Gantt chart  1. Title Write your thesis title in about 13 words. Just remember Friday the 13th if you have triskaidekaphobia . Or perhaps October 13 if you are a devotee of Our Lady of Fatima . As a rule of thumb, do not go beyond two lines for your thesis title in a given thesis template.  Remember that your thesis title is the first thing that the reader sees if they pick up your thesis on the shelf or search for it in your library catalog and online search engines like Google. A good title should accurately reflect the contents of your thesis. This is truth in advertising , since your thesis title is already an ad for your buyers—your potential readers, which includes your thesis adviser and panel members. Will they buy  your idea and read the rest of your proposal or your full thesis? Many marketing campaigns can succeed or fail with just a single se

Strike, dip, and rake directions in focal mechanism

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Vincent S. Cronin wrote A Primer on Focal Mechanism Solutions for Geologists (2010) . My interest in his work is in his descriptions of fault vectors and angles. I need to use these standard names if I wish to write a paper on Focal Mechanism of Earthquakes. Based on Cronin's diagram in p. 6, the reference strike, which we shall denote by $\mathbf e_{strike}$ appears to be the direction of the fault line as seen from a drone camera flying overhead high above the fault. The dip vector, which we shall denote by $\mathbf e_{dip}$, is a vector perpendicular to the reference strike $\mathbf e_{strike}$ and lies along the fault plane. The direction of $\mathbf e_{dip}$ is downward along the fault in Cronin. In this way, if we define the rake $\mathbf e_{rake}$ as the direction of the movement of the one side of the fault, then $\mathbf e_{rake}$ can be expressed as a rotation of $\mathbf e_{strike}$ about $\mathbf e_{dip}\times\mathbf e_{strike}$ by an angle $\theta_{rake}$, which is

How to use file folders to organize your documents

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I felt stressed. There were assorted documents stashed inside my bag. On my table lie some loose papers I haven't filed: they were sitting on top of notebooks in various stages of disarray. The file folders on the right side of my desk are arranged neatly, but I know at the back end are some documents that I haven't properly filed. And what was my filing system again? Entropy in Physics is a measure of the state of disorder of a system. According to the 2nd Law of Thermodynamics, the state of disorder of an isolated system can only increase. Hence, the mess. So I decided to overhaul my folder filing system. I sorted the papers into different folders. Each folder has a two or three level classification system. In some folders, I use the institutional categories. The is usually an institution, such as Ateneo (for Ateneo de Manila University) and MO (Manila Observatory). The succeeding keywords are just modifiers, e.g. "MO history CD" or "Ateneo faculty appoin

How create a journal notebook with date-time indexing system

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AT-A-GLANCE Planning Notebook with Reference Calendars, Plan.Write.Remember., 9.19 x 11 Inches, Black (70-6209-05) For the past few days, I experimented with a new research notebook: Kokuyo's B5 size Campus notebook. Its binding is flat, not spring. It has 60 pages. Each page has 35 lines spaced 6 mm. I chose the flat binding with glue because the notebook may be used as evidence for prior discovery in patent court proceedings. Loose leaf sheets are difficult to consolidate and present as evidence. Unlike normal logbooks with vertical red margins on the left side, I made my margins on the side opposite to the binding. The style is similar to that of a Tufte-style book , except that the margins are not too large, but only about 3.5 cm. So here's my system: There are no page numbers, but only dates starting at the upper corner on top of the margin column. The dates are in year.month.day notation, e.g. 20161017. But you may use the standard form, e.g. 17 Oct 2017. Each

Are you blogging for yourself or for your audience?

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Blogging for Creatives: How to Build A Blog Readers Love (Blogging Guides): 101 Questions to Ask Before You Launch Your Blog This blog is due for another overhaul. What keeps me up at night is how to properly classify my blog content. I am stumped with the following question:   Am I blogging for myself or for my audience? A. Am I blogging for myself? I can treat my blog as primarily for myself to define my personal brand. What is my personal brand? In Twitter and in LinkedIn, my tagline is Social Media and Space Weather Scientist. So my blog header should have at least two menu categories: social media and space weather . Or what I broaden the menu to media and science . I can add another one: teaching, but it's not in my main tagline. Of course, in my university, I am more known as a physics professor and less as a content marketer. This would create a triumvirate: social media, space weather, physics teaching . These three categories should be orthogonal: any article s

How to organize your tasks per hour, day, week, month and year using a plain binder notebook

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Trycooling PU Leather Loose Leaf Business Round Ring Binder Cover Notebooks 100 Sheets With a Pen Inserted (A5 6-Ring, Black) If you are riding a car, you see clearer the things that are near than those that are far. The far objects gives us a sense of direction, e.g. North, South, East, or West. On the other hand, the near objects give us warnings on whether we need to steer left or right. The same is true with planning: the long-term goals give us a general direction of our life, while the short-term goals are what we need to accomplish each day. There are many notebook planners in the market from detailed calendars with 30-minute resolutions, to general-type notebook planners with formatted days, weeks, and month pages. What I propose is just an ordinary binder notebook with unformatted pages for making short-term and long-term goals. You'll just do the formatting yourself. Here's how: 1. Get a binder notebook. I'm using 26-ring Septcouleur binder notebook, b

How to design your Twitter content mix by studying your audience

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I was looking at my Twitter audience profile and my audience's top interests are as follows: Technology (80%) Tech News (78%) Marketing (78%) Entrepreneurship (72%) Leadership (67%) Startups (64%) Business News and General Info (64%) Business and Finance (63%) SEO (58%) Advertising (52%) About 72% of my audience are male and 28% are female. All of them speaks English and they come from US (45%), Philippines (12%), United Kingdom (8%), Canada (5%), India (3%), and Germany (3%). A. CATEGORIES: TECHNOLOGY, MARKETING, BUSINESS Let's classify these topics into different categories that I think I can make a difference: Technology Marketing Business There are 6 permutations of these 3 words taken 2 at a time: Technology Marketing. How do we market technology products? I can tweet about the branding of Android, the pricing of chromebooks, the lifestyle behind Apple gadgets, etc .   Marketing Technology. What technology should we use use for marketing o

How your blog's name defines your blog content categories and tags

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The Renaming Handbook: How to Wisely Change Your Company Name, Organizational Name or Product Name Naming a blog is the first step in blog creation, whether in Blogger or Wordpress. A good name should be suggestive of the blog's content, with enough room to expand its coverage if needed. A bad blog name is a curse and it would require lots of advertising just to change its meaning or divert its association with something nasty or contrary to the blog's values or mission-vision. As a rule, a good name should not exceed 7 syllables, because that's the maximum number a human being can store in his short term memory. It should also not be too short to be meaningless, unless it's a brand name like Kodak or Adidas and you have lots of advertising dollars to spend. Below are some of my reflections on the names of my blogs, so that I know what to do with my blogs when I overhaul their their web designs and content classification systems. Perhaps, this exercise may be use

How content marketing differs from traditional advertising

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Content Machine: Use Content Marketing to Build a 7-figure Business With Zero Advertising After I posted an article on content marketing audit in my Facebook wall, a friend asked me: "What is content marketing?" I clicked on the reply button, typed a sentence, then another, until the whole thing became a paragraph. But I felt that it's still an incomplete definition. I really need to contrast content marketing with traditional advertising. So I deleted my reply and wrote this post instead. A. Traditional Advertising Picture this: It's a Sunday evening and you watch your favorite show in TV, such as football, drama, or cooking.  After a few minutes, poof! The show is gone and you see a gorgeous car, a lovely lady, a soap, a milk, or a a presidential candidate--all having nothing to do with the show you are watching. Your brain declares a red alert: it's an advertisement! You scrambled for the remote, and switched channel, hoping to find something interes