![]() The top and bottom of the blue curve are pinched together because the direction of the point moving along the circle is rapidly changing since the ellipse is wider than it is tall. For example, from the image above, you can tell the major axis is in the $x$ direction because the cosine analog has a greater range than the sine analog. I don’t know of any applications for this, but it is pretty interesting to see how the shape of these functions change depending on the characteristics of the ellipse. The blue curve is an analog of cosine, and the red is an analog of sine. In fact, if you set $a=c_0$ and $b=c_0$ in the graph above for some $c_0\neq 0$, the resulting functions will be the sine and cosine. This is analogous to the $\sin$ and $\cos$ functions for a circle. This graph shows the functions that yield the $x$ and $y$ coordinates of a point as it moves around an ellipse. ![]() The black curve is the function (you can edit it from the link above), the red line is the tangent, and the blue line is the normal. So I decided to create a little demonstration, and this is probably one of the first things that got me seriously interested in math. However, I did understand that the derivative magically yields the slope of the function at any given point. #DESMOS GRAPHING ART HOW TO#I also like it because I had no idea how to do calculus when I created it about a year and a half ago. I like this one because of the simplicity. To rotate an entire curve (as opposed to a single point), I made a parametric function of $t$ and applied the transformation to each point $(t, f(t))$ in the domain $a\leq t \leq b$. In the Desmos graph I took advantage of this fact to rotate each point. Luckily, the parameterization of the complex unit circle is exactly the same as the parameterization of the unit circle in the real plane (excluding the imaginary unit of course). Unfortunately, Desmos does not support complex numbers. This means a $z$ can be rotated about the origin $a$ radians by multiplying by $i^$) and $\theta$ is the angle of the same vector with the positive x axis. Note that this means each “point” is really just a single number. The blue curve is the original function and the orange curves are the rotated versions.Ī complex number $z=x yi$ is plotted in the complex plane by putting the real part $x$ on the horizontal axis and the imaginary part $y$ on the vertical axis. I accomplished this by first looking to rotations in the complex plane, then translating the method to the real plane. The goal of this graph is to take a function $f(x)$ and rotate it around the origin by an arbitrary radian amount in order to demonstrate the concept of rotation in the complex plane. ![]() You can click on the links after each header to edit and interact with the graphs in the browser. ![]() There are some additional interesting graphs at the bottom that are cool as well. Recently I went through my old Desmos ( ) graphs and I’d like to share 5 of my favorites here. ![]()
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![]() ![]() In case you’re using a Lightworks crack, there is no official agreement between you and Lightworks. If you can’t control the changes made to the program’s source code or at least tell which background computer processes are normal and which are suspicious, you can’t protect yourself from their illegal schemes. Through such malware, hackers acquire access to the files of your computer, obviously without giving you a warning or even a hint. By installing a free crack that is supposed to break the software’s defense, you are sabotaging your own safety. LIGHTWORKS PRO CRACK 12.500 HOW TOLearn more about how to get Lightworks for free.More often than not, it is actually cheaper to pay for the subscription, since illegal use brings harsh consequences. It might be that the unknown person is actually getting something they need from you only without honestly warning you about the fact. How likely do you find it that someone has worked hard to create a hack only for your benefit? Why Using Lightworks Crack Is a Bad Idea?īefore launching a Lightworks Pro, think again of what you’re really about to get. Lightworks_v14.5.0_full_64bit.exe ( download) Lightworks_v14.5.0_full_32bit.exe ( download) Wouldn’t you agree that safety and stable performance of the program is the top priority? In the meanwhile, you will be using a much inferior Lightworks crack, the functionality of which can’t be compared to the official version. You won’t know someone got access to your bank account and has been spying on your life through a webcam until it’s too late. Launching a crack undermines your computer’s security, thus making all the files on it accessible to hackers through a little hidden process that the crack has enabled. Those are usually called keygens but sometimes you see patches or loaders as well. LIGHTWORKS PRO CRACK 12.500 LICENSE KEYOne is to make a copy of the source code with required changes in.Īnother way is to create a small program that will produce a fake Lightworks Pro license key to unlock the official software. Hackers have two ways of achieving this result. A crack means an illegal copy of an official software changed in such a way that the verification mechanism is tricked into remaining inactive so no authenticity checks are performed. ![]() ![]() ![]() ![]() With react, you have easy access to things like styled components, Tailwind and thousands of other packages to help you make the website you want to make.Īnother reason for React is performance. The main reason I would argue, is that React makes your front-end development a much less painful experience, than trying to develop twig templates with some css and javascript files. Now some of you might wonder, why would I use React as the front-end for my Craft site, when I can just use Craft's built-in twig template functionality? Another difference is, that there are no premade templates to choose from. You can learn more about craft by visiting the Craft CMS docs.įor people who have used WordPress, the editorial experience is quite similar, with the difference being that you can choose yourself what fields your posts and pages will have. In other words, it's a content management platform where everything is customizable, and you're in control of your content and presentation. "Craft is a flexible, user-friendly CMS for creating custom digital experiences on the web and beyond." #Craft cms redactor codeIf something major changes in future versions, something in this tutorial might break or not work as expected.Īll the code for this tutorial is available on github. This tutorial was made with the following versions: You don't need to know anything about Craft CMS beforehand. I recommend having some basic knowledge of React, html and css, but complete beginners can also follow along. If there are punctuation marks in funny places or some weird phrases, I'll apologize in advance. I was inspired to make this tutorial to help you get started on your own Craft + React project by building a small blog site. I recently built a Craft CMS website and decided to use React as the front-end. ![]() ![]() ![]()
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