Category: Mathematics

Autism, Disability, Mathematics, Religion, Politics

Various links as indicated by the title of this post, the solution to one problem and a new problem. All topped off with the some photographs.

INTRODUCTION

This post features links, puzzles and pictures. The title refers to the subjects officiallly covered within the post. 

A NEW AUTISM RESOURCE

The Neurodivergent Rebel has produced a post that could become a goldmine. Titled “Web Resources” she describes it as a growing list and ends the post with this:

This is a growing list. Please send suggestions to NeurodivergentRebel@gmail.com

If you can think of anything to help the Neurodivergent Rebel expand this list please use the quote out above, which if you click on it will open up an email message addressed to her which you can then complete.

DISABLED PEOPLE ON BUSES

I have two links in this section. Firstly to a piece from Transport For All about Transport for London’s rExcl: proof faithless council, not union, to blame for Birmingham bin strikeExcl: proof faithless council, not union, to blame for Birmingham bin strikeesponse to the Supreme Court’s ruling on wheelchair priority spaces on buses. This piece is titled “First steps from TfL in response to Supreme Court’s ruling over the Wheelchair priority space on buses” 

Secondly, from Buzzfeed, comes this piece with the self explanatory title “Disabled People Say They Are Still Being Denied Priority Spaces On Buses Despite A High Court Ruling”.

TWO FROM THE SKWAWKBOX

The Skwawkbox is a regular source of excellent material, and these two pieces are no exception:

  1. BHAM COUNCIL MUST NOT BE ALLOWED TO SCAPEGOAT CLANCY TO RENEGE ON BIN DEAL – A follow up to the story that I reblogged from this site recently about a dispute in Birmingham.

  2. The second piece concerns the make up of the Labour Party’s National Executive Committee – the detail contained in the title “EXCL: PRO-CORBYN ASLEF, FBU TO TAKE NEC SEATS” means that at least for the present, and for the very first time, the NEC will have a pro-Corbyn majority. Here is an ASLEF related picture:
    Autism Acceptance Month

SWETA OJHA ON RELIGION

Sweta has produced an excellent poem titled “If Religion Schools You To War” and from it I quote the all-important final verse:

And if –
Religion still schools you to war
I, an atheist deserve an applaud.

MATHEMATICS

This section will include two links, the solution to one puzzle and a second puzzle. Both the links come from the Robert Loves Pi blog, and they are:

  1. A Zonohedron with 7802 Faces –  another of his remarkable constructions using Stella 4D: Polyhedron Navigator.

  2. A Four-Color Flag – exactly what the title suggests, and here is said flag:
    a four-color flag

PUZZLES

On Thursday in a post titled “Links, Pics and Puzzles” I included this puzzle:

Q

The solution is 96% + 96% of 4%. 96% of 4 is (4 x 96)/100 = 3.84. 96 + 3.84 = 99.84, os the answer is that if the death rate in surviving species had been the same as the overall extinction rate then 99.84% of all living things would have died in that event.

For my next puzzle I turn once again to Brilliant and offer up the following:

Marble Q

I will probably provide a solution on Wednesday.

PHOTOGRAPHS

Moorhen in algae

Nar Valley Park
Nar Valley Park – this development is now approaching completion.

gulls3

Town Hall
The next four pictures were taken on Thursday night – I had been acting as stand-in host on my aunt;s behalf, welcoming an airbnb guest to her house, and it was getting dark as I returned.

Lumiere 3Lumiere2lumiere1GullsGlaucous GullFlying cormorantmoorhens

Links, Pics and Puzzles

Lionks to various pieces I have found on the internet, an answer and solution to one problem and a new problem, and some photographs.

INTRODUCTION

This is a sharing post with some of my own stuff as well. I hope you enjoy it.

CROSSBOW BOLT STOPPED PLAY

Play between Surrey and Middlesex at the Oval has been halted and the ground has been locked down because a crossbow bolt was fired from outside the ground into the ground. Everyone at the ground is now in sheltered areas not out in the open. Armed police are now present at the ground. The match has now been officially abandoned, and a controlled evacuation of the ground is now underway.

SCIENCE AND NATURE

First a trio from wildlifeplanet:

  1. “Unreal Photos Of Animals From The Scandinavian Vicious Forest” – a piece highlighting the work of Finnish photographer Konsta Punka taking pictures of forest creatures:

  2. “Beach That Disappeared 33 Years Ago Has Reappeared” 

  3. “Here Is The Bird That Is Able To Fly For 10 Months Non-Stop (Video)” – a piece about the swift.

Hurricane Harvey has quite rightly received a lot of coverage. Here are three of the better pieces:

THE BEST BUS STOP

This bus stop is the subject of a post on illaboratoriodipleeny titled “Una meravigliosa fermata del bus….” that was brought to my attention by Anna, who was as impressed by it as I am. Here is the bus stop:

SOME POLITICAL PIECES

I start with a tool created by the Labour Party called the living wage calculator. You enter your postcode and it tells you how many people in your area would benefit from the minimum wage being increased to £10 per hour. Below is what is says about my postcode:LW

My next two pieces both come from the Skwawkbox:

A SOLUTION AND A NEW PROBLEM

In one of my posts on Monday I set a problem from brilliant. Here is I show the answer and an impressive solution. I also offer a new problem to end the section.

Thomas’ answer:

Screenshot 2017-08-31 at 5.51.15 PM

I admit to being lazy on this one – knowing that the internal angles of an octagon add up to 1080 degrees and that 7 x 90 = 630 I realised that with seven acute angles the remaining angle would have to be over 450 degrees, and the max is just under 360 degrees which takes you back to where you started. However 6 x 90 = 540 which means that the remaining two angles would have to add up to something in excess of 540 degrees, which is no great difficulty. Therefore I gave the correct answer of six (in less time than it has taken me to type this). However, one solver by the name of Atomsky Jahid produced a splendid effort:

Screenshot 2017-08-31 at 5.52.52 PM

A NEW PROBLEM

The mass extinction at the end of the Permian era is at the time of writing officially the largest in Earth’s history. An estimated 96% of all species on Earth at that time were rendered extinct. If the death rate in species that were not completely wiped out had been the same as the extinction rate what proportion of living creatures would have been wiped out in this event?

PHOTOGRAPHS

Guildhall
With Heritage Open Day coming up soon I decided to revisit these first two pics which feature thw town hall.

window

Greyfriars + wm
Greyfriars tower and the war memorial
Library
The library, taken today

P1040565

P1040566
A hald-moon in an early evening sky.
P1040564
The first of three closer up and enhanced shots of the half-moon.

P1040563P1040562Moorhen£2 - end of WWII

Science and Nature (and other stuff)

Some recent internet finds and some of my own photographs.

INTRODUCTION

This post features links to some recent internet finds and some of my own photographs. 

SOME SCIENCE AND NATURE LINKS

I start with a piece from mongabay which argues that “The Sixth Great Extinction” is actually “The First Biotacide“. Below is a picture from this article:

Steller’s Sea Cow holds the the world record for rapidity of extinction. Illustration from “Extinct monsters,” London: Chapman & Hall, 1896. Photo via Wikimedia Commons, licensed under CC BY 2.0.

The second piece in this section comes from thewildlifeplanet and is titled “Italian Super-Volcano Approaches Eruption“

PUBLIC TRANSPORT

I have five links to share in this section:

  1. vlogexpedition have a piece about the world’s longest railway journey – that along the Trans-Siberian railway.
    4 days on the Trans-Siberian Train
  2. My next piece comes from Vox Political, who got direct from the person whose story it is, Paula Peters. The title of the piece “Bus driver subjects disability activist to humiliating discrimination” gives you a good idea of the nature of the story. British law on this matter is unequivocal – the bus driver is legally obliged to give wheelchair users priority over mothers with buggies (this courtesy of a court ruling in January). Given the completeness of the information Paula provides, the bus company in question have only one option open to them both legally and morally – they must sack the offending driver and must make sure that all their drivers are aware of their responsibilities to disabled passengers.
  3. I am treating my last three pieces in this section together, as all are connected with London Underground, all come from indy100.com and all have been pressed on to my London transport themed website. They are respectively:
    “This is Officially the best Tube line”
    “    Quiz: Can you name the London Underground line by its colour?“
    “This gif exposes the lies the London Tube map is telling you”

FAB FOUR FINAL LINKS

First in this section comes a link to RobertLovesPi’s Blog for this piece titled “A Twisted Expansion of the Truncated Octahedron“, which features a very cool graphic. 

The Skwawkbox have produced an excellent piece titled “ATTACKS ON PIDCOCK SHOW MORAL BANKRUPTCY OF RIGHT – IN OR OUT OF LABOUR” Laura Pidcock is the recently elected MP for Northwest Durham and she has been making waves for her unashamed hostility to Tories and her criticisms of the cosiness and clubbiness of the House of Commons.

I started this post with a couple of science and nature related links, and now as we approach my photographs we are finishing where we started with stuff about nature, first of all Cindy Knoke with a wonderful post about a castle that has been dedicated to raptors, titled “Castle Rapture“.

With the last word before my photographs is Anna, who has recently posted part 13 of her amazing Paradise on Earth series, this time focussing on some of the smaller creatures who live in and around Trosa.

PHOTOGRAPHS

I will start this set of photographs with some of the smaller creatures I have recently captured, before finishing with some general pictures. These pictures were all taken yesterday.

white butterfly, yellow flowersTB on dandelion 3TB on dandelion2TB on dandelionBeeButterfly in nettlesButterfly and dandelionWhite butterfly on nettleWBTB1TBButterflybutterfly on nettleleaflike butterflyFlying buitterfliesred boattwo boatsBoatBoatsFlying gullmagpie 2magpie headmagpiesadolescent mallardMoorhen and chickMinis2Minis1Moorhen

 

Midweek Mixture

Some stuff I have seen recently on the internet, a little teaser of a problem and some photographs from today’s ‘ecotherapy’ session.

INTRODUCTION

I spent most of this morning indulging in ‘ecotherapy’ (i.e. getting out and about in the open air – my thanks to The Gentleman for the term), which also provide me with photographs which will end this post. In between times I will share various pieces that have caught my eye recently. 

NATURE AND THE ENVIRONMENT

I start this section with a petition that has been set up on thepetitionsite calling for Michael Gove to be replaced as Defra minister (see graphic below, which also functions as a link):

GOVE is bad for the environment. Demand new Defra Minister!

It is pretty much impossible for any replacement to be worse than the Downright Dishonourable Mr Gove, although while this dreadful government remains in office the right person for the job will not be selected. In the hope that Jeremy Corbyn, or someone who can influence him might see this I say, as I did when naming my fantasy cabinet a while back that the right person for this role is Caroline Lucas.

SOLAR POWER IN AUSTRALIA

It makes perfect sense for Australia to be looking at solar power in a big way, just as here in Norfolk we should take advantage of our biggest renewable resource by building many more wind turbines. I am therefore delighted to share this story from the treehugger website titled “Australia will be home to world’s largest single-tower solar thermal power plant“, the feature graphic from which I produce below:

australia solar thermal tower

THE DEATH OF THE INTERNAL COMBUSTION ENGINE

This is the title of a piece in The Economist. After 120 years of dominating the scene the internal combustion engine’s days are numbered, and the end for this pollution generating monstrosity cannot come soon enough. I include their feature graphic below.

A PLAN TO REVIVE AN EXTINCT SPECIES

This one comes from thewildlifeplanet.com and the species that may be being brought back from extinction is the Caspian tiger. The plan involves using DNA from the Siberian tiger, a rare but surviving species that is closely related to the Caspian tiger. A potential living area for the revived species has been identified in Kazakhstan. The map below shows the areas reckoned to have been inhabited by the common ancestor of these tiger species when it was around 10,000 years ago.

ANNA’S CHURCH

I end this section of the post with a nod to Anna and the brief post she put up yesterdya about her continuing fight to protect nature under the title “I went to my church“, one picture from which I reproduce below.

PUBLIC TRANSPORT

I am going to present these links as a bulleted list, amplifying some of them a little:

  • Our government has recently reneged on promised rail electrification programs in Wales and in northern England (yes, largely due to privatisation and consequent neglect our railways are so backward that not all of them have yet been electrified, some services still being run by diesel locomotives). Richard Murphy of Tax Research UK has put up a short post outlining how these electrifications could be funded.
  • The title of my next piece, from Buzzfeed, should be sufficient: “People Who Use Wheelchairs Are Being Forced To Crawl On To Trains And It’s 2017“
  • The last piece in this section come from the skwawkbox. The first features a video from Double Down News which referring back to an incident from last year is utterly devastating for Virgin Trains, as it shows conclusively that Jeremy Corbyn was telling the truth when he described that train as ‘ram-packed’ and Virgin’s subseqnet denials, including one from the boss, Richard Branson, were lies. The most devastating footage comes about halfway through the video, which is embedded below, and shows the reserved seats filling (as one might expect) moments after Corbyn had walked past them. The skwawkbox piece is titled “DOUBLE DOWN VIDEO SCOOP PROVES WHAT WE TOLD YOU LAST YEAR: #TRAINGATE WAS FULL“.

ELECTORAL REFORM

Britain’s First Past the Post (FPTP) system of electing representatives has had its day. Those who support this system claim that it delivers stable majority governments, but it has failed to do this three times running (no majority in 2010, wafer-thin majority for Cameron in 2015, May running a minority government with the support of the vile DUP in 2017. I have three recent pieces dealing with this topic for your attention. 

  1. Setting the scene for the other two a post on theconversation.com titled “Wasted votes, hyper-marginals and disillusion: reform group issues damning report on election 2017“
  2. The Electoral Reform Society’s introduction to their full report titled “June’s election was the third strike for Westminster’s voting system. It’s out” and…
  3. The full report itself, titled “The 2017 General Election: Volatile Voting, Random Results“.  

As well as the voting system needing reform, the results in Northern Ireland showed that it is time for the Labour Party to abandon its pact with the SDLP and field candidates of its own – the recent Stormont election successes of Gerry Carroll and Eamonn McCann have demonstrated that non-sectarian socialists standing as such can win in Northern Ireland.

A PROBLEM AND SOME PHOTOGRAPHS

I generally finish my posts by putting up some of my own photographs. Before getting to those I have a teaser for you:

coin tosses restricted

The above table shows two putative sets of coin toss records, each for one coin tossed thirty times. Which is more like to be genuine based on what you can see?

a) series one
b) series two

If you want to have a public stab at answering this feel free to use the comments, although I will say neither yea nor nay until I put my next post up, which will include an answer to this little teaser. 

Now for those photographs…

featureimageTortoiseshell3flying butterfly

Mother and child
The junior duck in this picture is just developing her adult feathers, but continues to be chaperoned by her mother.

Moorhen2Moorhen1White butterfly3white butterfly2PollinatorTortoiseshell2Tortoiseshell1white butterflyCH2CHMini waterfall

 

 

Answer to the Pythagorean Problem

The answer to a problem incliuded in yesterday’s post Monday Miscellany.

INTRODUCTION

You may remember that in yesterday’s post titled “Monday Miscellany” I included one of the problems I had solvced on the mathematical website Brilliant – this post presents the solution and also clears up a side issue raised on that website by disgruntled folk who had got it wrong.

THE PROBLEM

Here is the problem again from yesterday:

Pythag

THE SOLUTION

The answer is True. The formula for (x+1)^2 is X^2 + 2X + 1, and every odd number greater than 1 could serve as the 2X+1 part of that equation. 

THE SIDE ISSUE

Some people on Brilliant cavilled at this because there are some Primitive Pythagorean Triples whose smallest term is even (8,15, 17, 20,21,29 and 65,72,97 were all mentioned, although none of the complainers mentioned 12,35,37, 60,91,109 or 696,697,985). The question did not state that the triple of which the odd number is the lowest term was the lowest triple to feature that number, and indeed if one looks carefully at the triangles presented as part of the problem one can see clearly that the odd number is allowed to be in another triple where it is not the lowest term:

Pythagorean Triples Solution - a

Note that the number 5 features twice (ringed in the diagram above, once as the largest term in a triple and once as the smallest).

Thus that 15 features in 8,15,17 does not invalidate the claim of the question since it is the smallest term in 15, 112, 113. All the other odd numbers mentioned in triples of which they are not the smallest member likewise feature in triples in which they are the smallest member, the biggest being 985, 485112, 485113.