Email required Address never made public. Thus it is always of negative. Equation Solver Solve equations with any number of variables in them - all you need are the coefficients for each variable and some time. This is a must have For Algebra 2 students. That sinks our chance of getting a tidy mathematical formula. This program does FOIL for arbitrary degree functions I. This portfolio thetw formed out of the share of.

My list of engrossing side projects get longer year after year. I have tinkered with mobile apps and Unity assets of late. This time a ghost from my past became the focus. Long ago, Put option theta formula x sheer co-created a package, GRTensor, for the symbolic math package Maple to do calculations for general relativity GR. It has continued to be used by a small group of relativists who find it useful for off-loading the horribly tedious calculations that come up in curved formulaa.

In the intervening years Maple has changed significantly and the package was becoming difficult to install and was basically unusable on Macs. I got back to GRTensor because I was going to use it do some simple calculations for geodesics on two-surfaces for a Unity asset — but I discovered as a Mac user that this was not going to work out.

After exchanging a few emails with Maple, they agreed to extend me a multi-platform license so I could look into fixing up this mess. I contacted my collaborators and we pulled together the source code. Initially I planned to **put option theta formula x sheer** a bit of diversity in my week and mix in some time on a second project, learning some new drum riffs and reading. With a specific project and goal in mind, and only a week I ended up coding 10 hours a day.

I was able to zone in to the point where I would look up from my morning coffee to discover it was lunch time. Twenty years ago, we build GRTensor around the idea that tensor objects in GR could be constructed algorithmically. If you decide you want to define a tensor Foo, then the package created variables for Foo and auto-generated code to calculate Foo based on the formula used to define it.

LOTS of global variables. In order to make GRTensor fit into the modern Maple package paradigm, with GRTensor as a Maple module and good citizen in the eco-system, the globals in the Module needed to be defined and scoped — and not created on the fly. This led to a LOT of fairly mundane changes to push the objects into a wrapper, which in turn is scoped. A bit of Python scripting made this not too terrible.

Other quirks we exploited in the 90s no longer worked in the modern Maple and hunting these down took additional time. Another chunk of work required changing all the user input prompts to adapt to the new dialog-based input used in Maple. Lots of interactive testing. After blasting on this for a solid week — I now have a decent beta offering that will get tested by a few researchers. Hopefully GRTensorIII plus source code will be open for use by the end of the year.

I had a great time and got a big feeling of accomplishment from the week off. Sabbatical week is an excellent idea — which I now plan to make an annual event. In developing Gravity Engine I learned a great deal about high pedigree N-body simulations, but in some cases e. There is WordPress JS bug when this animation and a YouTube link are present] Creating code to move a planet in an elliptical orbit with the correct velocity is surprisingly tricky.

This is one of those cases where you might expect you could just grab a formula from Wikipedia and bang out some code. Historically, this angle is named the True Anomaly. Here a picture will help: The eccentric anomaly is NOT the same angle as f in the picture however they can be related with a bit of geometry:. If we have a specific time we want a position for we need to convert this into a value of M. This is done by dividing the time by the time per orbit, T.

Kepler can also help us here with his third law that relates the size and eccentricity of *put option theta formula x sheer* orbit to the mass of the bodies: where m is the combined mass of the central object and orbiting body. Kepler did not know the proportionality constant was the mass, that came later.

E appears by itself and inside the sine function. That sinks our chance of getting a tidy mathematical formula. This equation is legendary in Mathematics, since it is an early example of a transcendental equation with for,ula import application. There are some series approximations, but they are not valid for optoin eccentricities. I have left out some of the init code for clarity.

If you view the source for this page you can find all this. For bodies at rest this is probably impossible although I am not aware of a proof. In the case of my app, in most cases it was an artifact of the simulation. Start with two bodes at rest a fixed distance apart, attracted by gravity. They can only get as far apart as they started assuming they started at rest. If two bodies interacting do fly apart — it is an artifact of the simulation not coping well with the very large forces at close approach.

This is commonly done in scientific-grade simulations but in game physics is not typically demanded since the collision usually results in some form of destruction. As usual, I started by buying more physics books and downloading papers. This convinced me that I did need to have a regularizing algorithm and also showed me that doing one from scratch would take some time. These programs are BIG and generally written in FORTRAN or C and I was hoping to continue to use C within Unity.

It was about one thousand lines. As an added bonus I would gain a much deeper insight into how the algorithm worked. ThreeBody now uses the TRIPLE engine and the encounters continue to be very fascinating — even more than before. For masses with no initial velocity it is still difficult to find long lived solutions. There is also a higher pedigree non-regularized Hermite integrator for comparison to Leapfrog. A large gallery of very cool three body solutions is now part of the app.

Ranging from solutions found by Euler and Lagrange in the s to those found as recently as These are hypnotically beautiful — even though not all of them a stable. Broucke On Relative Periodic Solutions of the Planar Three Body ProblemCel. Very comprehensive, detailed formu,a of algorithms. A readable, wider ranging overview of N-body simulations and the behaviour of star clusters Roy Orbital Motion, CRC Press Derives Euler and Lagrange three body solutions. One of the classic texts sueer orbital mechanics.

This is all in FORTRAN. The TRIPLE thetaa used in ThreeBody is derived from the TRIPLE code thetx. The Hermite integrator offered as an option in ThreeBody is a modified version of an integrator in Starlab. One of the great things about meetups is their ability to generate weird idea exchanges. This mapping creates a space that is a topological torus.

This was the spark I needed to arahan tangguh forex review more carefully about what motion on a real torus would be like. One of the problems that comes up in such studies as a way of sharpening skills is the study of motion on curved 2D surfaces. It is a great place to learn to use the mathematical machinery and intuitive enough that the answers can be visualized. First we need a mathematical description of the torus.

It is a 2D surface so only two co-ordinates are *put option theta formula x sheer* to describe a point. The radius of ;ut center of the torus is and the radius of the cross section is. In the mathematics for a torus, everything can be described in terms of these co-ordinates, including the equations of motion that define how an object moves when there is no force on it.

We are accustomed to thinking of the torus as a three dimensional object but exactly which three dimensional shape results is partly due to the choice tbeta when we embed the surface in 3D. There is really no reason we have to do this but it can help our intuition. This allows us to map into the x, y, z world co-ordinates the game will use and retain our intuitive picture of a torus.

Frmula about a 2D map of this torus? The embedding equation provides the world space position to show events on the torus. What equations should be used to calculate motion on the torus? On curved surfaces things are different. To make this clear lets consider a simpler 2D surface, the sphere, with longitude and latitude.

As you know from looking at maps of airplane flights, the lines between points take what seem to be curves on the map. This is because the force-free or geodesic path that connects two points is a great circle. This means if you are in New York and head directly west the geodesic path must be a diameter of the circle and will carry you into the southern hemisphere until you are at the antipodal point directly opposite New York through the center of the earth.

You started out with only a velocity in the direction but ended up on a trajectory for which also changed. The equation for the evolution of depends on the velocity in the direction. The expression are finite. Never a great idea. This is not a fundamental part of motion on a sphere, there is no special place where acceleration goes to infinity.

It is quite usual to have to cover a surface with several co-ordinate patches. For the torus we are lucky that this is not needed. The equations for on a curved surface come from a branch of mathematics known as differential geometry. This is because each point has its own tangent plane more generally tangent space. Returning to our sphere example, if you initially were heading west from New York when your great circle crosses the equator you are no longer facing west BUT you did not turn, you were just following your geodesic path.

Exactly what the geodesic path is and how it turns as you go is something that can opption calculated for a surface. Here the odd paths of the objects make the impact of the curved surface apparent. The primary one is that the size of objects in the 2D and 3D view cannot be fully reconciled more below. On the true mathematical surface the distance travelled as you walk around the thetw diameter is different from the inside diameter.

I did put this in the game as an option — but the result is a put option theta formula x sheer odd looking. In normal play this mode is disabled — with the consequence that the objects on the screen are not exactly the correct size. True pption leads to some weird paths in the map view. If an object is moving quickly in the shrinking due to the scale factor can exceed motion towards the edge making it look as if the object backs up a bit before continuing on. It has been great fun to think about and use the geodesic math I learned long ago.

There was a time when I knew about this stuff. However, there is a trick I used in undergrad when I decided that I wanted to have the option of going to graduate school, that applies here. I am using it to get my physics kung-fu back. In high school puut was easy to pick up. I do not speak much else. Efforts to learn French, Spanish and Mandarin at various points in my life have all been tedious and I have never managed to get very far.

Although I speak math, I was a **put option theta formula x sheer** student. In first year I was so **put option theta formula x sheer** to the bottom of the class, that I doubt anyone below me returned for the next semester. I did manage thetq squeak up to being 30th percentile — and I would have told you I was working hard. For the entire term I was either in tueta or at my desk.

I did every question multiple times. I filled in every gap in the derivation in the text books. I went back and repeated start to finish questions I had not gotten right the first time, until I could take a blank sheet of paper and get it right. This book is a tour-de-force, beginning with Newtonian gravity, detouring into shapes due self gravity and tidal forces, three body orbits and then heading into techniques to model general relativity and gravitational waves in situations where full blown general relativity cannot give direct answers.

Back to the trick. It is NOT any easier. After a fifteen year break, I have spent more forex broker company newsletter a few hours reminding myself about div, grad, curl and lots of other forgotten math. Put option theta formula x sheer progress is slow, but not painful. Chapter 1, question 1 took me two weeks.

As I feel knowledge seeping back I am excited to discover the connections and see where physics leads. Chapter two is going a bit better, since I now have some of my math skills back. I have returned to N-body, my first mobile effortwith the goal of making it cross -platform and adding new ideas. This has a very tempestuous history in software and is one of the things Joel Spolsky thinks you should never do. Ttheta of the things I made a note of when I read the more academic of these books was the formkla three body problem.

The question is: can three bodies be placed in initial conditions with zero velocity such that they will stay in a bound configuration? As I get more kung-fu with Unity and formyla the leap frog integrator I had ported for Nbody this kind of side project becomes very do-able. Another addition for the ThreeBody app. It is weirdly addictive and a good way to see how sensitive the problem is to initial conditions. Hope someone out there also finds it fun.

There is some further technical detail. I will never use the old OnGui again! I have been shfer the new framework for the past several months while Unity 4. During this time I have collected a few tidbits on working with the framework. I found the tutorials on Canvas, RectTransform, Button and Event System a bare minimum to get the idea of the **put option theta formula x sheer** thing. There are two things that are important to know.

The crucial other element is adding a CanvasScaler to your root canvas. As the device screen size change your UI element will scale appropriately. In the C world the Unity elements can be created and modified as you would expect. You will want one or both of the following includes: The ThreeBody game I am creating makes use of collections of buttons as radio boxes.

I set the disabled and highlighted colors to reflect the color I want for unselected and selected. When it is time to enable a button, then the normal color of the button is set to the value in the highlighted color. It would be reasonable to expect that: would work. Instead you need to make a temporary copy of the ColorBlock and syeer modify its elements and otion back the ColorBlock: Button touch events will still fall through into code that handles touches so it becomes important to screen out those touches that are over top of buttons.

A technique that works for both mouse and touch events is: There is not a lot said about panels in the tutorials or online docs. Formu,a appear to be containers for holding a subset of the UI being developed. I found them useful for Settings Menus and High Score panes. This needs to be done at the formkla of the fade out or the start of the fade in optikn the object to stay visible during the fade.

This is not part of the new Unity UI theme but as part of getting ThreeBody ready I had to learn a bit about TrailRenders. I always had weird issues with setting materials and colors until I finally found some clear advice on the forums about the material shheer. Another tidbit is how to recycle objects once you have used trail generation. To get rid of the trail I ended up setting the trail length to -1, then counting 5 update cycles before setting the object inactive and putting it back into my object pool.

I played around with coroutines for this but they ended up creating more complications — and a simple synchronous design won out. One way I cling to the notion that I still know something about physics is to create oddball mobile physics optipn. Since this is a side-project my goal is to spend theha of the time on physics and less on the time-intensive UI tuning.

I have moved to Unity and while learning Unity I decided to try and make a mobile game inspired by a spinning magnet office toy I had had for years. In my initial enthusiasm for Spinor I decided that adding leaderboards would be a good idea. It would encourage people to share their love of my awesome game and take me on the road to self-sufficiency as an indie developer. This meant that I needed to add code to track login state and provide options on the level select screen and game over screen.

I found a way to spooge it in. The level select screen was one of those things that is not the fun part of developing the app, and I had just plopped in some touchable tiles and some hacky strings using the Unity OnGUI approach. I then decided this was a great time to search the Unity asset store. I put option theta formula x sheer discovered the Mad Level Manager and decided to grab it when it went on sale.

The end result is a cleaner looking game that is more presentable. The idea for the game came from watching my kids play with the BuckyBall magnet toys on a coffee table — taking turns placing them and trying to keep them apart. The interactions were put option theta formula x sheer and dynamic. It seemed a great choice of the kind of app I put option theta formula x sheer to write — lots of physics. This is my entry in an internal hackathon at work.

The development did take some interesting turns that I may now have time to blog about. I have spent three years of spare time to create a single App. It was very satisfying to be completely curiosity driven. This was a complete departure from the ruthless pragmatism that informs the way I code in my day job. The dev team knew what they were doing and what the company really needed me to do was articulate our vision to customers and analysts.

As a result I found I had traded in Eclipse for Powerpoint and Word. After a while I found that I really missed the kind of problem solving that comes with developing pit. At the time iOS was really hot and a hobby project in this area seemed like a good idea admittedly, not an original thought. When I get a blank sheet of paper I generally do something relating to physics.

I had the great fortune to evolve from an undergrad in engineering into graduate degrees in physics. Good advice — and apart from a sojourn in graduate school my software skills have been how I pay the bills. It seemed natural to try and link compare software forex trading youtube and gravity in some way. The journey started with something not too different from the old Java code from long ago.

I got some basic iPhone code running with Quartz graphics added a bit of touch interaction and simple gravity evolution. It was ok but seemed a bit uninspired. At seer time there were people in the startup doing graphics stuff. They kept talking potion shaders and GPU code and I was curious about their world. I also thought it would be cool to make the gravity simulation do proper 3D.

At this point Forex trading fbs games probably had invested about five months optoon iOS to get the Quartz game going. I decided to press reset and start again in OpenGL. Vormula OpenGL up and running was a BIG deal and caused at least a six month hit. It takes a while zheer have the right mental model of what is really going on in the shaders and without a graphics debugger using only newbie knowledge I ended up doing a huge amount of experimenting.

I was able to get some reasonable 3D stuff going. After all I was also trying to get some chops in Objective-C. However, I had running code and started to work on the touch interface and game flow. During this time, in my day job, I had realized I just did not have the temperament to pitch for a startup and wave the flag day after day. I aheer a senior software role in a mature forex trading machine reviews youth and started to wade through their code.

It is hard to adequately convey how bad this code was. This had repercussions in N-body. This resulted in some significant refactoring in N-body. Then iOS5 came out. It had GLKit routines for math and utility routines for texture loading at put option theta formula x sheer time when I was just starting to realize forrmula values of texture atlases. I found it very useful to revisit design patterns in the context of Objective-C. Another big bonus was a colleague who had a long history in MacOS development and was generous with his time.

I also used this opportunity to go all the way to the bottom in OpenGL. Since I had no strict self-imposed deadline I messed around with how vertices were generated, how the lighting in the shaders work, normal maps for texture simulation, how to map strings into textures into transparent objects, and on and on. Once iOS6 came along the Xcode OpenGL debugging became much easier. That feature in Xcode is hugely powerful. I really wanted to show these orbits in the co-rotating frame and find a way to interactively generate some intuition about how variations in starting conditions affect the orbit.

This added more time to the development. Then I stumbled into the choreography orbits. This sent me on a detour to learn more about choreographies and change the physics engine to do fourth-order Runge-Kutta evolution. Finally, it seemed like a good idea to have built-in autoplay for all the optoon — so I could regress after making changes to the integrator.

This took a further investment in time but one which on reflection was time well spent. I found a number of issues during these regression tests. Then it was time to polish. This is a challenge for me. I have a half dozen other cool physics game ideas and a shelf of unread books. Somehow I managed to stay focused and get N-body done to a level that I felt I could stand behind.

There are things I wish were better, levels I wished I had time to add but I forced myself to just record all the diversionary ideas and bond put option definition esoteric two and half years stop wandering off and stop the feature creep. After some reworking and a bunch more polish I deemed it was ready to submit.

Enter your email address to subscribe to this blog and receive notifications of new posts by email. Home ThreeBody ThreeBody 2. There is WordPress JS bug when this animation and a YouTube link are present]. Creating code to move a planet in an elliptical orbit with the correct velocity is surprisingly tricky. I have attached the subscript F to the angle to indicate this is the angle **put option theta formula x sheer** the focus of the ellipse between the position of the body and the long axis of the ellipse.

Where is time in this equation? Here M is the position of a body moving in a uniform circle at a constant rate that we will relate to time and E is the angle to the position seher the ellipse from the origincalled the eccentric anomaly. Here a picture will help:. The eccentric anomaly is NOT the same angle as f in the picture however they can be related with a bit of geometry:. Kepler can also help us here with his third forex trend trading method 1 methodology that relates the size and eccentricity of the orbit to the mass of the bodies:.

Given M, Solve for E. Determine the orbital period T. Find the corresponding r using the orbit equation. Forty year optipn FORTRAN to the rescue! Close Encounters Have Near-Infinite Force. For those who want to delve further an annotated reference section is provided. Aarseth, Zare A regularization of the three-body problem. A readable, wider ranging overview of N-body simulations and the behaviour of star clusters.

Roy Orbital Motion, CRC Press Derives Euler and Lagrange three body solutions. It almost killed me. I learned by doing, using the material in the book to solve problems. I got into grad school. Back to the present…. I have decided that I refuse to feel nostalgia and loss about this topic. I need to learn it.

This may take some time, but optuon trick is working again. Adapting for Shedr Screen Sizes. UI interactions with Scripts. You will want one or both of the following includes:. ColorBlock: Changing Button Colors. The ThreeBody game I am creating makes use of collections of buttons as radio boxes. It would be reasonable to expect that:. Instead you need to make a temporary copy of the ColorBlock and then modify its elements and copy back the ColorBlock:.

Touch Events and Buttons. Button touch events will still fall through into code that handles touches so it becomes important to screen out formla touches that are over top of buttons. A technique that works for both mouse and touch events is:. Panel Fading and CanvasGroup. There is not a lot said about panels in the tutorials or online docs. D example of such a fade coroutine is:. Hope some of these save you some time. Google will take pretty much anything. Within hours my app was up on Ptu Play.

They give the best feedback. Potential is now available on BlackBerry World and Google Play. The result can be seen here:. Okay, I think I get where the three years went. Available on iOS, Android and BB. Proudly powered by WordPress.

## Managing Stock Option Positions

Value at Risk for Derivatives and Monte Carlo Simulation. Theta 1 for a put. To estimate the value of the option in. The three barycentric coordinates of x, he versatile option hoice. binary option theta formula sheer size of this binary option money management. To fix this problem you will need to put your browser in Another option for many of the "small All reduced cheat sheets contain the same information as the.