Category Archives: General

General

Personal review...

I've been thinking a little (probably too much lately) about happiness and what I need to try and improve over the coming year so that I don't run into next Christmas the fizzling wreck that I did this year.  I'm not quite sure if I'm honest why I found last year so demanding, I know I've taken a lot on, but I know people that work much harder than me and manage to tick along quite happily.  However, what I need this year is a plan so that I don't end up unravelling by the time I hit Christmas...
223:365 - Unravel...

Perhaps it's the stress of the new house and trying to get that constructed or perhaps it's still my inability to adjust to life as an academic (I still find working in the public sector a massive culture shock compared to the private sector) or perhaps I just need to cut back on the number of activities and groups that I'm involved in.  Whatever it is, I'm finding it hard to get back into the swing of things and I need to start pushing forward.

I'm a big fan of LifeHacker and whilst there is probably an equal measure of articles that I find myself raising an eyebrow or to at in disbelief or disdain, there are a few little gems in there that are quite helpful.  One thing that seems to have been a recurring theme on the LifeHacker blog is the idea of undertaking a personal review of the previous year and see if that shows any patterns.

I'm going to search around for a template and see what I can conclude from a personal review, I'm not sure if I'll share the results of it on here or not, but I'd be really interested to know if anybody else does something similar at the end of the year?

General

Dual Monitors...

For years I ran dual monitor configurations on my main PC for gaming and found that the extra space that the second screen afforded me was invaluable, although for some strange reason I never really transferred this logic over to my preferred working environment.  Well actually that's not entirely true, I actually ran two machines, a Windows machine and a Linux machine side by side with each performing different tasks.

Since starting my PhD, one of the first things that I wanted to get setup was a decent laptop for writing and modelling on so that I can literally work anywhere.  My colleagues tell me that I'm 'idea rich' but 'time poor' so I need to be very opportunistic about how I work and write if I'm ever going to stand a chance of getting close to completing my PhD.  Don't get me wrong I still use fountain pens and notebooks a lot too for when I'm just too impatient to wait for things to turn on and boot up...

023:365 - Journal...

I've tinkered and meddled in true engineering fashion and now I think I've got a fairly stable writing environment setup that works for me, I use Scrivener for papers and articles to get the framework of the idea set out and then do the final push in Word 2011 (although a warning to other users disable autosave on the Mac version as it has a habit of killing and corrupting your files).  For my figures and diagrams I flit between OmniGraffle Pro and Visio 2010 Pro.

For referencing I use EndNote x4, I know that it's currently on version x6 but I've got x4 spanning between a Windows environment and a Mac environment using a common database that is shared via dropbox, it works perfectly, and so until someone utters the words "Congratulations Dr Currie you passed your viva with no corrections" I'm not changing it... even if one of the Minogue sisters came round on bended knee begging me to upgrade, it's not happening... if both Minogue sisters turned up simultaneously however I may start to waiver...

But the downside of having a laptop is the limited area that you have to fit in all of these different windows etc on a single screen, of course one of the beauties of a UNIX based system such as MacOS is the different workspaces you can have configured, but sometimes you need everything in one space.

To overcome this I bought a cheapish (£90) 22" monitor with HDMI connection (with a TB to HDMI lead) for my office so that I can have a reference document or EndNote library up and running in the secondary monitor and my writing document in the primary window.  So far it's working well, I'm finding it is making my life a little easier, particularly when I want to merge two documents together into a single document, copying and pasting between the two when writing and combining my lecture notes into larger handouts.  One of the key things to consider though when picking a second monitor is get one with an identical or similar resolution to your primary monitor so it makes moving your cursor between the two painless, if the resolution is different then sometimes the mouse can get caught at the top or the bottom of the screen where the resolutions are just off.

I'm finding that the dual monitor configuration is really helping my writing, I spend a few minutes setting up the documents and then I can throw myself into my writing.  Of course if I find myself on the train or in a coffee shop with half an hour to spare or so I can still write and seize that opportunity to write on my laptop on a single screen, but the dual screens is still my preferred way of writing... there are a few articles kicking about the internet that extoll the virtues of double screen writing and how your productivity will double, I can't vouch for the doubling in productivity but it might just make your life a little easier with your various software packages competing for screen footprint space.

 

General

Born free...

Having had a few conversations with engineers in person and on Twitter, it would appear that those that have coded or written complex spreadsheets all advocate that young engineers should make the time to learn at least a simple programming language or some other means that lets them model a problem through a construction they've made themselves rather than a packaged piece of software.  The ability to write your own analysis routine to test for various variables is invaluable when testing out a new structural system, or even for automating tedious calculations.  If you're really clever you can get Mathematica to do fancy things like the animation below in a single line of programming code.

The downside is that some of the packages to let you do this can be quite expensive, even for academic licences.  Whilst a student licence of MatLab can be purchased for about £30, grabbing a copy of Mathematica or MathCAD is going to set a student back around about £90.  If you're a practicing engineer then you're going to have to purchase a full licence which is going to be about the £1,000 mark.

So if you've never programmed or written code before in one of these sorts of languages, that can be quite an investment and one that could be seen as a bit of a gamble.  For example, most of our water engineers within the department swear by MatLab for manipulating large matrices and from the reading I've done it would appear to be much quicker than Mathematica on very large matrices, but speed is only half the story.  If speed really was the biggest concern, then users would write code in Fortran, C, or even the newish language Julia.  Personally I've never really got on well with MatLab, it just feels quite clunky to learn and I prefer to use Mathematica for tinkering and meddling with bits of code, it has lots of mathematical routines embedded so I'm not wasting lots of time writing routines to invert matrices etc and I can just get on and write.

I know that lots of engineers in industry are quite positive about MathCAD, but again this is an expensive program to purchase, particularly if you're not sure if it's what you need really and just fancy having a tinker about with it to learn.  If only there was a free version perhaps?  Well there is! In the form of a program called SMATH Studio which is very similar to MathCAD and is free to download and use, which has to appeal to your inner Yorkshireman if all you want to do is try and see how to use a piece of software like this for creating your calculations and a few simple models.  In fact it also has the ability to let groups work on the same sheet and collaborate in real time which is great if you're working on a session and there's an ocean inconveniently between you or you want to show someone else how to do something specific in the software.

If you're more mathematically minded and want something that has a bit more grunt with symbolic mathematics, then again there are various free packages out there and one that received warm praise is called SAGE.  I can't pretend that I've used it in anger myself, but it appears to create a local server that you edit files through a browser session on and several other PhD students I know all sing its praises.

But once you've created mountains of data from your laboratory testing and you want to undertake some statistical analysis, most institutions would reach for SPSS but the student licensing costs for this are mental compared to other pieces of mathematically focused pieces of software and from memory they're on a term by term basis as well rather than a perpetual licence.  This is where free alternatives such as the R project come to the rescue and their increase in popularity is gathering momentum with really good quality text books being published to help users learn statistics and the software in one fell swoop.

The added bonus for me is that these pieces of software are available for PC and Linux, so if you've an old computer kicking about that you don't know what to do with, then throw on a copy of Ubuntu and breath in some life to your old machine and start tinkering and messing with these bits of software... if you kill the computer through excessive tinkering, then it doesn't matter, simply repair, rebuild, and carrying on meddling... it's the best way to learn.  Particularly when there's no money to be lost as all of the software is free, you just need an existing computer, some time, and a desire to have a go.

General

Writing...

I've been reading a couple of blog posts about other students' writing environments (both digital and physical) and the I've been really interested in the approaches they take when it comes to software selection but I've really been struggling to follow why they go to such extraordinary lengths to set up bespoke writing environment.  We have a few mathematicians associated with our course and they all swear by how LaTeX, for example, saves them days and days of typing equations and how they couldn't possibly write any of their materials without it.  But the part I'm really struggling to understand is that it was created about 40 or so years ago to overcome typesetting problems and surely there must be something more effective available now after all this time?

002:365 - My brain hurts...

Whilst I have a copy of Scrivener and I'm used to writing large batch files in Vi and ViM from my days using SPARC SunOS stations, I still choose to do most of my writing in Word.  It has an outlining tool which I find useful, but the deal sealer for me is that I can make it dance when it comes to large documents with regards automation.  Through simply using styles and captions, I can have a simply written and elegantly cross referenced document up and running in seconds.  Whilst scrivener is intended to get your ideas down on a page and get writing, I just don't feel that it's quite there for technical documents, as figures should be numbered and cross-referenced, as should equations and I'm far too lazy to do this myself and I've sort of gotten used to Word doing the donkey work for me for the past 20 years on these elements.

Admittedly the equation editor is dreadful in Word and is to type-setting what I am to men's ballet.  I've overcome this though by using MathType 6.7 which makes all of my equations look uniform and well typeset, with the added bonus of having numbering macros and scripts embedded into Word that allows me to automatically number equations and cross reference them in my writing.

Another boon for using MathType is that I can colour code equations, something that might sound trivial, but actually can be really useful in presentations to grey out parts of the equation that you're not interested in for the minute or for making critical terms bright red to make them pop out on the slide whilst you discuss them with the students.  I know you can do this too with LaTeX as that's the technique that I use for embedding equations in this blog, but I create the equations first in MathType and then after I've pasted them into here I simply edit a few colour tags.

To be clear, I'm not criticising anyone's writing setup, the key to writing is finding something that works for you.  But there does seem to be a trend on several social media sites to push for methods of writing that avoid mainstream packages.  I understand that money is tight nowadays and every penny counts, but I've managed to get myself a copy of MS Office and Mathtype together for about £60 all in, I'm sure that it can be done cheaper using something like LibreOffice that comes pre-installed with Ubuntu, but I take the view that £60 is less than an hour of my charge out rate when I was in industry and doing it this way will save me countless hours.

I do like peeking into other student's writing environments, both physical environments and their digital environments, but I'd love someone to explain to me why I should adopt LaTeX over Word and MathType, particularly given that I'll be embedding a lot of vector graphics from OmniGraffle and Visio and I'm really struggling to see how these other sorts of environments will help me write more efficiently, but then I guess it's horses for courses...

General Research Tutorial

Cable-Chains...

Part of the work that I've been undertaking on Mathematica is to create a series of sheets that will calculate the geometry of a cable-chain arch with a set of given parameters.  In part I’m interested in how the cable-chain arch can behave as a deployable structure and looking to build on the work of (Li, Vu, & Richard, 2011) to see how practical a cable-chain structure can be made with regards economy, efficiency, and robustness.  Essentially a cable-chain structure is a curved arch that is sub-divided into straight sections, with cables spanning across the base of two struts as can be seen in the figure below.  Simple versions of these types of structures are widely used for the likes of temporary and deployable aircraft hangers to create large open spans.

Pantographs

Now that I’ve got the makings of a simple Mathematica sheet up and running and I’ve taught myself some rudimentary programming and graphics manipulation skills I’ve managed to start to knock together what I feel are some high quality illustrations for my thesis.

I’ve done this with a mixture of Mathematica to create the base diagram, which I save as a PDF.  I then import the PDF into OmniGraffle to annotate the diagram and then export to a PNG file to maintain the transparent background, this figure I can then host for linking into blogs etc.  Below is a sample figure which shows how the number of segments (nSeg) affects the internal area available for habitation within a typical parabolic arch.

Cable Arches

Given that both of my brothers are colour blind and I’ve never done the test, I’m not convinced on my choice of colour schemes, but the good news is that it won’t take long to change if it turns out I’ve made my figures look like something off the set of Austin Powers.

So far I’m finding OmniGraffle quite limited compared to Visio that I’ve been using for my diagrams for perhaps 20 years or so.  I decided to use OmniGraffle though as most of my writing work is done on a Mac, although I also have a PC so I can always create the more complex diagrams on Visio if need be, especially as I’ve managed to get a legitimate copy from work for £12.

I'd love to hear how other engineers and academics approach creating technical figures and sketches on their Macs though, I've a feeling that I'm really missing out on something and there's got to be a much slicker workflow out there.

References:

Li, Y., Vu, K. K., & Richard, J. Y. (2011). Deployable Cable-Chain Structures: Morphology, Structural Response And Robustness Study. Journal for the International Association for Shell and Spatial Structures, 52(168), 83-96.

 

General

Time...

Now that I'm through the massive pile of end of term marking and I'm starting to think about getting some research done through the summer, this goes hand in hand with time management skills.  I spend a great deal of my time in unstructured activities supporting students during term time, so during semester 3 I become quite hard nosed about the time slots with students.   Once I've made my list of things that I've got to do, then I'll typically I'll go for a quick win and tick off some of the easier things to give myself a sense of initial progress. With the remaining tasks then I create a Gantt chart to programme out the works through the summer period to see if I'm being overly ambitious with my intentions.

Screen Shot 2012-06-30 at 08.04.36

Once I've protected my time and planned out my summer work, then the next step is simply doing it...

I have to confess to being one of the great procrastinators and I have a couple of techniques that work well in getting me up and started on tasks and I encourage my students to make use of these techniques to help them keep on top of their dissertation writing, the two techniques I use are: the pomodoro technique & breaking the chain.

The pomodoro technique makes strategic use of an egg timer when working on tasks.  The notion is that you set the timer for an initial 25 minutes and then work single mindedly on your selected task for those 25 minutes, nothing else is allowed to distract you from that single task, no telephone calls, facebook, twitter, house fires (well maybe house fires)... but on the whole you just work on that one single task until you hear your bell ring.  Once the bell has rung then you can give yourself a five minute break, make a brew, make a quick phone call, whatever you need to do... but then you set the timer again for 25 minutes and crack on with the next step of your task, or the next task and repeat this process 4 times.

Once you've completed 4 sessions, give yourself a longer break, half an hour, an hour... that part's up to you, but what you're likely to find is that you've been super productive for the two hours that you've running the pomodoro technique and actually taking an hour off at this point might be needed to let your brain cool down... it just depends how hardcore the tasks are that you've been doing.  One tip here though is to set a timer for your breaks, otherwise they will over run.

I use a mixture of timers when working with the pomodoro technique, either a cheap mechanical timer from Sainsbury's which cost £3, a pomodoro mac app that puts completed pomodoros into iCal that I can't link too here as it's no longer available in the UK for some reason, or pomodroido on my phone.  If you're the sharing type, you're likely to want to broadcast your pomodoro sessions over Twitter or your social media network of choice... please be aware though, this is really annoying for those of us not working on your tasks so please exercise some discretion.

125:365 - Pomodoro...

The next technique I use is called 'break the chain' essentially this is about doing a little and often and requires you to have a big wall planner or calendar on your wall to be the most effective.  Say there are long term goals that would benefit from doing a little work on them, but regularly.  If your task would benefit from doing a little and often, and you can slowly work your way through to completing the whole task in this fashion, then the break the chain technique is perfect.  I first heard about this from a LifeHacker article I read which attributes this technique to Jerry Seinfeld.  Basically if you want a tidy house, to progress your PhD thesis, and get fit each of these tasks require constant effort to achieve.  You can't necessarily do them in monthly spurts, your house would become messy between bursts of effort, your thesis would become disjointed and rushed, and you're likely to have a heart attack when attempting your monthly marathon.  However, if you were to break these down into smaller tasks, you'd be amazed at the results that you could develop.

013:365 - Calendar...

Firstly let's say that every day you spend a minimum of 10 minutes cleaning, 30 minutes writing, and 20 minutes doing exercise... that's an hour you need to squeeze in every day.  But when you do these three tasks you are allowed to put a big fat black cross on your calendar, preferably in a fat marker pen to be highly visible.  Every day you do these tasks, you earn a big fat black cross on your calendar... the key is to make the longest chain of crosses possible...  Try and keep your daily tasks below 60 minutes to allow them to be achievable, but simply do them... 10 minutes of tidying every day will strangely make a large difference to the tidiness of your house and 30 minutes of writing, whilst in itself isn't a lot... but it helps to keep your hand in on writing and stops you going a whole week without having done any!  ( A common curse for PhD students).  20 minutes of exercise every day could be something as simple as heading out for a walk that day, you can vary the level of intensity to suit.

I'm not pretending that this would be all you'd need to do to keep the writing up, but by doing 30 minutes every day that's 3.5 hours of writing per week, that could be a few thousand words you never would have had being there in your thesis ready to edit and sculpt into some sort of tangible form when you've time to edit.  You're still going to need to make writing a priority during your working week, but at least your brain and fingers will be well trained in making a start after your core sessions each day.

I'm hoping this helps someone a little out there, either through sharing the apps that I use, or giving some food for thought on how a little and often can be a real boost to your productivity.  If you've found anything helpful, please drop me a line or leave me a comment.. if you've another technique that works for you or have an immunisation for procrastination I'd REALLY like to hear from you...

General

Summer loving...

Well, having completed my first complete academic year, I'm now entering into semester 3 and I need to start planning what it is that I want to achieve over the summer whilst most of the students are away.  There's a common misconception it would appear, that academics all bugger off to Tuscany for the summer running care free and naked through the hills with the wind blowing through their hair, finally returning in September to teach again.

Macclesfield Forest Panorama...

The truth of the matter is that this is perhaps the only time in the year when we can actually get stuff done that we want to, we've access to the laboratory and we're able to crank through all of those things that we've just not had opportunity to get round to through the academic year due to other pressures.  The key to getting things done though is to create a list of what it is that you want to achieve... so here's my list (in no particular order yet as I need to put timescales next to them).

  • Review COMSOL and attend a training session.
  • Develop a series of Mathematica sheets for calculating geometry.
  • Learn ANSYS.
  • Learn Inventor.
  • Update lecture materials for the MSc and some of the first year modules.
  • Write 2 chapters for my PhD.
  • Complete my Lynda.com training session for Blackboard 9.1.
  • Completely re-populate all of my Blackboard area, embedding Mathematica.
  • Complete WriteTEL2 programme with Napier.
  • Write resit papers and mark any resubmissions from repeating students.
  • Obtain ethics approval for my innovative structures teaching programme.
  • Finish two journal papers.
  • Become registered as a STEM ambassador.
  • Complete a 'Meet the Engineer' session at MOSI.
  • Arrange next year's Technical Lecture Programme for the IStructE
  • Complete my examination marking for the IStructE
  • Complete the Advanced Structural Behaviour Exam paper for the IStructE.
  • Submit draft textbook outline to McGraw Hill.
  • Define a solid workflow for creating technical illustrations, MS Visio or Adobe Illustrator.
  • Explore Wolfram SystemModeller.
  • Find and create a pool of study buddies...

In amongst this I've also a significant build on with our new house, although we've a good builder on board so hopefully it shouldn't drain too much of my time.  I also intend to take some time out for a holiday, as well as doing some hill walking with a little landscape photography thrown in too.... but here's the rub... when I look at the list above I find myself thinking that's quite a lot of stuff to fit in through the summer months, but the difference being that actually I find the activities listed above good fun and I've actively taken on board these activities through my own volition... they're not crap that has been dumped on me by an inconsiderate boss.

This ability to be highly self-indulgent is perhaps the thing I like the most having joined academia, although I still feel guilty come every Friday when I've not completed a timesheet... but just to be able to make time in my own diary to head off and read about something I find interesting is incredibly liberating...

General Tutorial

Arc...

Following on from my last post where I was investigating how to determine the parabolic equation when only provided with three co-ordinates, I wanted to extend that knowledge and create a Mathematica sheet to allow me to do this without having to rely on Wolfram Alpha.  This is for two reasons, firstly if I don't have an internet connection, then I'm screwed as Wolfram Alpha isn't going to work for me... secondly I need to encourage a deeper understanding of the procedure and process if I'm going to get the most from Mathematica.

Screen Shot 2012-06-03 at 19.22.03

The first part is trying to determine the parabolic equation when I know three points on the curve, typically these are going to be the start, midpoint, and the end support point.  To give an appreciation of the geometry, it's important to firstly understand that parabolic curves are defined by the common equation:

f(x) = a{x^2} + bx + c

Determining the length of a parabola with cartesian co-ordinates is done through applying the equation below over the limits being considered.

Length = \int\limits_a^b {\sqrt {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} dx}

As three co-ordinates are known along the curve, the equations can be expressed as follows, with (x1,y1) (x2,y2) (x3,y3) being taken as the co-ordinate points... this gives a nest of simultaneous equations that can be solved using traditional matrix methods or in this case elimination could be used given that one of the input variables is 0.

\begin{array}{l} ax_1^2 + b{x_1} + c = {y_1}\\ ax_2^2 + b{x_2} + c = {y_2}\\ ax_3^2 + b{x_3} + c = {y_3} \end{array}

 Taking the co-ordinates above as (0,500) (2050,0) (4100,500) for the input variables, this gives the simultaneous equations below to solve:-

{a{{\left( 0 \right)}^2} + b\left( 0 \right) + c = 500}

{a\left( {2050} \right)_{}^2 + b\left( {2050} \right) + c = 0}

{a\left( {4100} \right)_{}^2 + b\left( {4100} \right) + c = 500}

However, Mathematica is well equipped for solving simultaneous equations and simply requires that the expressions are stacked up neatly and logically.... there can be a few problems with mixing bracket types, but this is just down to practice.  To solve the simultaneous equations above, the following code will solve them, the double equals signs are used just to push up the accuracy of the expressions and Reals is used as an additional parameter just incase any of the solutions are imaginary numbers.

Solve[{a x1^2 + b x1 + c == y1, a x2^2 + b x2 + c == y2, a x3^2 + b x3 + c == y3}, {a, b, c}, Reals]

Which will return the following solution:-

a = \frac{1}{{8405}};b = - \frac{{20}}{{41}};c = 500

Substituting this back into the general expression determines the parabolic equation for this particular curve to be...

f(x) = \frac{{{x^2}}}{{8405}} - \frac{{20x}}{{41}} + 500

The last thing to do is to work out the length of the curve between the two support points, this is a simple process determined by:-

Length = \int\limits_0^{4100} {\sqrt {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} dx}

For those of us with too little time on our hands, this calculation can easily be automated and defined within Mathematica using the following code, where f'[x] is used to differentiate the term within the brackets.

f[x_]:=500 - (20 x)/41 + x^2/8405;

NIntegrate[Sqrt[1 + (f'[x])^2], {x, 0, 4100}]

Which gives the length of the cable to be  4,257.24m  which matches Wolfram Alpha's answer perfectly... the next step is defining equal length links to segment this curve to start creating the geometry for parabolic cable-chain structures... that's definitely a post for another day.

The intention with this post is to help anyone who is trying to define parabolas and arc lengths using Mathematica... or traditional methods, if they've got time on their hands...

General

Geometry...

I've posted a few times that I feel my mathematics skills have slowly atrophied having been out in industry and that this I feel will be my achilles heel when it comes through to my research.  One of the areas that I've been investigating is the relationship between cable-chain structures and their behaviour.
Screen Shot 2012-06-03 at 16.40.54
Depending on how many segments you divide the arc into will determine the geometry and efficiency of the cable-chain arch, now if it's a semi-circle that's not too hard to calculate the geometry using simple triangles.  In degrees the internal angle of each triangle will be given by the following formula, where nseg is the number of segments you're dividing the arc by:-

Internal{\rm{{ \,\,}}}Angle = \frac{{180}}{{{n_{seg}}}}

This then can allow you to calculate the length of the segment along the arc as set out below using the Cosine rule which I haven't used for probably about 20 years, this though is only half the problem as you still have to determine the length of the cables.
Screen Shot 2012-06-03 at 18.42.40

Length = \sqrt {2{R^2} - 2{R^2}Cos\theta }

Length = \sqrt {2{R^2} - 2{R^2}Cos\left( {\frac{{180}}{{{n_{seg}}}}} \right)}

Next to determine the length of the cable, you will need to combine two of the triangles previously calculated and which gives double the internal angle and repeat the process for the cable that is shown highlighted in red below.
Screen Shot 2012-06-03 at 18.42.56

Length = \sqrt {2{R^2} - 2{R^2}Cos\left( {2\theta } \right)}

Length = \sqrt {2{R^2} - 2{R^2}Cos\left[ {2\left( {\frac{{180}}{{{n_{seg}}}}} \right)} \right]}

This all seems fine and well for simple circles, but how would you know that a semi-circle gives the most efficient arrangement for a cable-chain?  What about if it's a parabola?  Well fortunately for the mathematically out of practice determining the equation for a parabolic curve is pretty easy for us Mathematica users...  Let's say I know I have a draped cable that spans 4100m horizontally between supports and has a 500m drape at the middle.  We can define three points on this cable easy enough as can be seen below:

Screen Shot 2012-06-03 at 19.22.03
This is where Mathematica starts to flex its muscles for me and why I feel I get good value from the student version that I've purchased.  I don't know what the Mathematica code for determining a line through the points is, but if I press the = key twice I get access to the Wolfram Alpha Servers and try and describe using every day English what it is that I'm trying to do...  Following a blog post from Mathematica on determining arc lengths using calculus I tried the following term which doesn't use any mathematical code at all, simply describes what it is that I'm trying to do:-

Parabola through the points (0,500), (2050,0), (4100,500)

Which gives the me the following output, which is pretty helpful to the maths novice who is trying to explore and understand the relationship between the data, the expression, and the graph...

Screen Shot 2012-06-03 at 19.29.49

Which makes my life a lot easier as I can start to tinker with geometry very quickly now using this approach.  One of the cool things about working this way is that you can then start to dissect the code and determine what the correct format should be when creating Mathematica sheets and it makes learning Mathematica much much easier than say MatLab or Maple.

Whilst creating code like this would not be difficult for someone with a little rudimentary programming experience, it isn't that intuitive for a newb like myself, but now I can start to adapt this syntax to suit what I need...  The next step is to try and work out how to subdivide this into nseg number of equal length links... but that's a job for another day.  Maybe I'll need to start using polar geometry to make my life easier? Who knows... but at least I'm not being held to ransom by my elderly fuzzled brain anymore and I can explore and play with the maths rather than being pummelled by them.

I'd love to hear from other Mathematica users, especially to hear what their experiences are and particularly to hear if I'm missing a trick as I'm going through and learning the syntax...

General

Patterns...

One of the challenges when researching in an engineering field is to determine what patterns your data may present you with.  This can be an unfamiliar skill for those of us that have come from industry as we're used to dealing with certainty when designing buildings, not uncertainty.  One of things I've been messing about with lately is patterns and series of numbers as I've been learning Mathematica, using Roozbeh Hazrat's book to help.

Bokeh Basket...

This has let me calculate the palindromic prime numbers less than 10,000 and other long winded sums in a single line of code.  It has had me thinking about other series of numbers such as the Fibonacci series which is present in nature and Pascal's triangle... (below)  I've been seeking these types of patterns and puzzles out to try and sharpen my powers of observation and help with rebuilding my maths skills which have atrophied over the years.

\begin{array}{c} {\rm{1}}\\ {\rm{1\, 1}}\\ {\rm{1\, 2\, 1}}\\ {\rm{1\, 3\, 3\, 1}}\\ {\rm{1\, 4\, 6\, 4\, 1}} \end{array}

Pascal's triangle is quite a simple pattern to determine, you simply work through the line above and it helps you create the next line below in the series.  Take the first number, it's always 1, then add the first two numbers together on the line above to get your next number, rinse repeat to see what you get...

\begin{array}{c} {\rm{1}}\\ {\rm{1 1}}\\ {\rm{1 }}\underbrace {{\rm{(1 + 1)}}}_2{\rm{ 1}} \end{array}

In the example above when you add together the two numbers on the second row, you get the number 2.... I've highlighted this with a bracket on the example above to illustrate how you get the number 2 on the third line...  try working through this process to see if you can get the pattern above to repeat and see if you can follow the logic.

Now this is all fine and well, but Pascal's triangle is well known and it isn't going to win you a bet down the pub... the Aha! moment that goes with puzzles is the key to a successful puzzle (Badger, Sangwin, Ventura-Medina, & Thomas, 2012)  the simpler the explanation, the more readily the solution will be accepted (Michalewicz & Michalewicz, 2008).

So following the pattern theme of this post, let's see what we can make of the following pattern and see if it can help sharpen up the old grey stuff... and if you crack the puzzle, maybe you can try it down your local and see if it earns you a free pint...

\begin{array}{c} 1\\ 1{\rm{ 1}}\\ {\rm{2 1}}\\ {\rm{1 2 1 1}}\\ {\rm{1 1 1 2 2 1}} \end{array}

What is the next line for this pyramid?  If you're struggling and would like a hint, then try saying the series aloud.

The solution is 3 1 2 2 1 1 because there are THREE ONES, TWO TWOs, and ONE ONE on the line above...

If you're struggling to solve this puzzle, then you can highlight the text from this line to the line above to reveal the answer.

References:

Badger, M., Sangwin, C. J., Ventura-Medina, E., & Thomas, C. R. (2012). A guide to puzzle-based learning in STEM subjects. Birmingham: University of Birmingham.

Michalewicz, Z., & Michalewicz, M. (2008). Puzzle-based learning: An introduction to critical thinking, mathematics, and problem solving. Melbourne: Hybrid Publishers.