What I changed in 2020

This page details what I've been working on lately, so that you can find recent changes to my site. It's entirely possible that some links on this page shall fail to work, or fail to live up to their descriptions: that just means I haven't checked in (recent changes to) the pages they referred to as recently as I've updated this page. This page omits things separately covered by the thoughts of the moment section of this site, unless I update one after its moment: this page is about on-going development on the rest of this site.

This was the year of Covid-19 (and the one in which The Liar got fired), which kept me home more than usual, but that didn't really increase my enthusiasm for writing. I also didn't find the enthusiasm to go running and my weight rose to 110 kg in the summer, although I did manage to drag it back to 105 kg by November. I was obliged to get a head-set to join in with on-line calls, which made it possible to spend way too much time watching videos, so quite a few pages gained links to relevant interesting ones.

Inequality around gender

An essay on something we all know happens. Part of some broader thoughts on privilege.

On discovering mathematics

or inventing it; and its remarkable efficacy, either way.

Unifying wealth and income

How these and other forms of power can be tied together as just the aspects at different time-scales of a common theme.

Simplices and smoothness

Split out part of my study of simplices into a page devoted to their rôle in smooth manifolds and related contexts.

Relate the Sine rule to the circumcircle's diameter

and noted another proof of the Sine rule.

The Euler line

and a fair bit of reworking of my study of the various centres of a triangle.

Add some C++ code

for my exploration of computing sporadic entries in Fibonacci's sequence.

More on logarithms

Split the discussion of logarithms off from that of powers and exponentials.

Power series

A cursory and incomplete introduction.

A rant about reality

and why most arguments about what it is are hot air.

Another property of pythagorean triangles

The incircle is a whole-number multiple of the highest common factor of the sides, when they are rationally commensurate.

Numerals with fractional parts

Specified the extension of natural numerals to include handling fractional parts for rational numbers (and, implicitly, their use to approximate reals).

Added a memorial

to John Horton Conway.

More details on Platonic solids

Finish up an earlier exploration of what's possible with a mixture of faces (but all vertices the same); gave tidy co-ordinates for vertices; and restructured.

More BF&I

An example of how, with a little careful thought, I discovered an elegant solution to a problem, that I initially solved by ruthless use of cartesian co-ordinates and algebra.

How (not) to mark up names

A quick rant about something I've seen done wrong rather often.

Chord Envelope

The nice smooth curve that arises from a bunch of straight lines, connecting points on two lines, whose end-points all have the same sum of distances from where those two lines meets.

A brief look at discrete simplices – or, equivalently, partitioning a counting number total as a sum of lists of counting numbers.

Characterising Continuity

Checked in a rumination I'd written a while ago and tried to make it a little less wooly.

Ptolemy's Theorem

A proof of a non-elementary but powerful property of cyclic quadrilaterals. Also noted a neat consequence of the intersecting chords theorem and moved that discussion to its own page.

Earlier history
2019, 2018, 2017, 2016, 2011–2015, 2010, 2009, 2008, 2007, 2006.

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