A Mixed Bag for Monday

Solutions to my last two maths problems, some sciencey pieces, a petition and some photographs.

INTRODUCTION

This post includes solutions to the problems I posed on Saturday, and a few other things from various sources. 

SPACE STATION DODECAHEDRON

Here is the question as a reminder:

Space station Dodecahedron

Here is the answer:

Dodecahedron answer

Here is a splendidly concise solution from David Vreken:

Vreken route

A VARIARION ON THE MALFATTI THEME

Here is the question:

Malfatti Mistake question

Here is the answer:

Malfatti Mistake answer

In the 19th century Malfatti conjectured that the way to maximise the area of a triangle you could fill with three circles was to fill in the three largest circles that touch specifically two of the three sides. Although he was not alive to be humiliated it turned out that he was not merely wrong, his proposed solution has been proved not to work for a single triangle. The solution that always works is first put in the largest single circle that touches all three sides that you can, then fill in the largest circle you can in the remaining space and then do so again. In an equilateral triangle the difference is small, but in a long thin isosceles triangle it is quite substantial. 

Here is Jeremy Galvagni’s published solution:

Galvagni outdoes Malfatti

SCHOOL REFUSAL SYNDROME PETITION

This on the official site for petitions to the UK government, which means that you have be a UK citizen to sign it. Please click the screenshot below to sign and share it if so minded:

School Refusal

A TRIO OF SCIENCE PIECES

First a fascinating piece from the National Geographic titled “Can Today’s Whale Species Survive the age of Humans” which covers the past and present of the cetaceans and speculates about their future. 

David Quammen, a good writer and a useful scientist to know about if you are planning an A to Z post, has a new book out on the subject of evolution, and Jerry Coyne of whyevolutionistrue has provided a very detailed review of it.

Finally, a letter to the Guardian signed by 60 well known environmental campaigners declaring their unwillingness to debate with climate change deniers, and why they are unwilling to do so. Below is the opening to the letter (please click to visit the original) and a list of signatories:

Guardian letter

signatories

SOME FINAL PHOTOGRAPHS

To finish here are some of my recent photographs:

Sea birdsFlying cormorantBlackbacked gull lands on the waterCormorant and rowing boatCormorant and sea birdsWingspanMoorhenCormorant

 

 

 

Author: Thomas

I am branch secretary of NAS West Norfolk and #actuallyautistic (diagnosed 10 years ago at the comparatively advanced age of 31). I am a keen photographer, so that most of my own posts contain photos. I am a keen cricket fan and often write about that subject. I also focus a lot on politics and on nature.

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