2020 Newsletter: 17/54 — PreviousNext — (Attach.)

Sydney Harbour

Hello and Welcome,

Meetings This Week:

Programming - Tuesday Apr 14th - 5:30 pm (6:00 pm meeting start) - 8:00 pm

This will be a Zoom meeting. Regular attendees will receive details by email.

Steve OBrien,
SIG Leader.

Web Design - Saturday Apr 18th - 1:30 pm (2:00 pm meeting start) - 4:00 pm

This will also be a Zoom meeting. Regular attendees will receive details by email.

Steve South,
SIG Leader.

Meeting Next Week:

Tuesday Forum - Tuesday Apr 21st - 9:30 am (10:00 am meeting start) - 12 noon

[ Meeting cancelled until further notice. ]

Current & Upcoming Meetings:

23 2020/04/04 — 14:00-17:00 — 04 Apr, Saturday — Penrith Group
24 2020/04/14 — 17:30-20:30 — 14 Apr, Tuesday — Programming SIG, L1 Woolley Room
25 2020/04/18 — 13:30-16:30 — 18 Apr, Saturday — Web Design, L3 Norman Selfe
26 2020/04/21 — 09:30-12:30 — 21 Apr, Tuesday — Tuesday Forum, L1 Woolley Room
27 2020/04/24 — 09:30-12:30 — 24 Apr, Friday — Digital Photography [ Discontinued ], L1 Woolley Room
28 2020/04/28 — 17:30-20:30 — 28 Apr, Tuesday — Main Meeting, L1 Carmichael Room


“ASCCA News to Use, Peruse and Amuse”:

Easter greetings to you all. Well here it is the ASCCA NEWS, to use, peruse and amuse! [ See attached four-page PDF file — Ed. ] ASCCA brings you a collection of interesting and helpful options to remain connected with family and friends, learn different ways of doing the things you like to do and generally stay sane in these trying times.

Please distribute to all of your members. I am sure that all clubs have worked out the best ways to keep your club alive and active even though the clubroom doors are closed. This ASCCA NEWS is to help you keep in touch with all of your members — forward it now!

Take care, stay safe, fond regards,

Nan and Jenny,

Nan Bosler, AM

Jenny Willcox,

Australian Seniors Computer Clubs Association
Level LG, 280 Pitt St SYDNEY 2000
(02) 9286 3871

ASCCA acknowledges the traditional owners of country throughout Australia and their connection to land, waters and community.
We pay our respects to them, their cultures, and to their elders past, present and emerging.

Tech News:

“Schools and Companies are Banning Zoom Due to Security Concerns”:

See the ReviewGeek article by JOSH HENDRICKSON | @canterrain | APRIL 6, 2020, 10:34AM EDT.

Across the world, more people are working from home than ever, which naturally calls for more video conferencing. Zoom, a popular video conferencing solution, started as a winner in the fight for mindshare, but that's slowly turning to a loss. After multiple privacy and security concerns cropped up, companies and schools are starting to ban the service.

It certainly hasn't been an easy time for Zoom either; just the other day, it promised to pause feature updates to work on its security issues. That's likely in response to the news that it sent data to Facebook about you, even if you don't have Facebook. Or perhaps leaking user info is the problem. It might be the fact that Zoom's custom encryption method is flawed. Or the problem might be that it may be sending data through China.

The list goes on, and that's why schools and companies are starting to ban Zoom from employee use. The bans began with SpaceX and Nasa but quickly spread. PDLT-Smart sent out an internal memo banning Zoom, and not long after, Nevada's Clark County school district banned Zoom.

Now New York city also issued the same directive to its schools. And Washington state's Edmonds School District and Utah's Alpine School District are considering similar bans.

Zoom rose as a popular service thanks to its ease of use. So long as the host has an account and the desktop software, anyone else can join a call without an account or software. But now it may be time to rethink what service to use in the future. To that extent, Skype can handle group calls even when no one involved has the software or an account.

Read more »

“Windows Update Notifications Changing”:

See the Infopackets article by John Lister on April, 8 2020 at 01:04PM EDT.

Windows 10 users will soon get slightly clearer notifications when an update is ready. They will also get a reminder of the risks of updating a laptop running on battery power.

The notifications will appear in the Windows 10 Action Center, located at the bottom right of the screen.

Scheduling Updates Easier

As well as telling users an update is ready, it will give the chance to click on one of three options.

Two options are already familiar: to update immediately ("Restart Now") and to delay the update until later that night ("Restart Tonight"). The latter option simply reschedules for an unspecified time when the user is less likely to be using the PC.

The new option in the notifications will be for the user to specify a specific time for the update ("Choose an Hour"). That's already possible to do, but currently involves digging around in the "Settings" app and therefore isn't as convenient or clear. (Source: mspoweruser.com)

Another change includes a new animation of a laptop being plugged into a power outlet. That's designed as a reminder that users should avoid updating Windows 10 on a machine that's running solely on battery power.

Empty Battery Could Cause Problems

It's important to avoid the risk of the computer shutting down unexpectedly in the middle of an update.

The reasoning here is that it could corrupt the update as it's being installed, which then causes serious problems with the operating system itself. In some cases, a severely corrupted update may require a complete reinstallation of Windows. (Source: techradar.com)

The new notifications should start showing up with Windows 10 version 2004, expected to roll out next month. While that's the technical title of the relevant update, it's more likely to be known publicly as the Windows 10 May 2020 Update.

It will be the first of two major updates this year to Windows 10. Major updates include new features and changes to the GUI (graphical user interface), rather than minor tweaks and security fixes that ordinarily roll out across each month.

Read more »

Fun Facts:

“Sines and Cosines — Some Exact Values — Part II”:

Last week:

Sin 30° and cos 30° have exact values, namely 1/2 and √3/2. See the "half-equilateral" triangle which is a 30°, 60° 90° triangle and then use Pythagoras.

Sines and cosines of some other angles have much more complicated values.

Some can be calculated using the double-angle formula: sin(2θ) = 2sin(θ)cos(θ), for example.

See several dozen exact values for sine and cosine with angles up to 90° displayed on this page by Julian D. A. Wiseman.

In fact, every multiple of 3° up to 90° is included in this table.

This week, we add a further interesting step in this chain.

See the paper: The Sine of a Single Degree by Travis Kowalski.

Travis Kowalski is a professor of mathematics at the South Dakota School of Mines and Technology. His academic interests include complex analysis, applications of power series, and the cultural and historical roots of mathematics. He also enjoys drawing cartoons and visual wordplay, spending time with his family, and panicking at the ever-increasing size of his "to do" list.

“Though the radian is the undisputed king of angular measurement in calculus, required as it is for the familiar trigonometric derivative and integration formulas to hold true, it is the degree to which most of us are first introduced. The humble degree — one three-hundred-sixtieth part of a complete rotation — is one of the oldest methods used to measure angles. Its use dates to antiquity and it can be found in ancient Babylonian, Greek, Indian, and Mayan mathematical traditions. Many theories have been suggested for its ubiquity, ranging from the astronomical (a solar year has approximately 360 days) to the practical (360 has lots of divisors), but the fact remains that the degree is, if not a mathematically ideal way to measure angles, a particularly human way to do so.

In a typical trigonometry class we devote time learning those special angles that admit exact trigonometric ratios involving roots of integers, such as 30° and 45°. A question that might interest students of trigonometry is whether this is also true of the archetypal measure 1°? That is, is its sine expressible as a ratio of some combination of radicals and integers? Can we compute the sine of a single degree exactly?

The answer to this question is "yes," but the path to computing it meanders through classic geometry, polynomial algebra, and complex numbers. The purpose of this paper is to follow this path to the value of sin 1° and to see some beautiful mathematics along the way.”

“The two most familiar isosceles triangles are the equilateral (60-60-60 degree) triangle and the right-isosceles (45-45-90) triangle, from which the familiar sine formulas sin 30° = 1/2 and sin 45° = √2 / 2 follow immediately.

Another important triangle, less familiar to us nowadays but was well known to the Greeks, is the golden triangle: the isosceles triangle whose base angle is twice its vertex angle. We use this golden triangle to compute the sine of 36°.”

Finally, we get that sin 18° = (√5 - 1) / 4 and cos 18° = √2 · √(5 + √5) / 4.

Last time we found sin 15° = √2 · (√3 - 1) / 4 and hence cos 15° = √2 · (√3 + 1) / 4.

If we know the trig functions at two angles, we can get the functions at their difference by the formulas:

sin(α - β) = sin α · cos β - cos α · sin β,
cos(α - β) = cos α · cos β + sin α · sin β.

Combining the values of sin and cos 18° with sin and cos 15° we can work down to 3°:

sin(18° - 15°) = sin 3° = sin 18° · cos 15° - cos 18° · sin 15°

= ( √2 · (√3 + 1) · (√5 - 1) - 2 · (√3 - 1) · √5 + √5 ) / 16

= 0.0523359562­4294383272­2118629609­0784187310­1825394016­4920483509­3815998571­0464175…

“This is just a stone's throw away from sin 1°, but sadly, that is as close as we are going to get using only the Greek geometer's tools of straightedge and compass. None of the Greek geometers — or indeed any of the geometers to come after — could find a straightedge-and-compass construction that would yield 1°.

It would not be until centuries later that such a construction was shown to be impossible, a consequence of the powerful algebraic theorems devised by mathematicians in the 18th and 19th centuries. Perhaps the most relevant result to us is the following: An angle of integer degree measure can be trisected if and only if it is a multiple of 9°. Since this is not true of 3°, we cannot construct 1°.

It is possible to algebraically manipulate trigonometric identities to solve for sin 1° as the solution of an equation [ they involve roots of a cubic equation — Ed. ] rather than as the length of a side of a very specific triangle.”

Sin of 1 degree
Sin of 1°

Here, courtesy of WolframAlpha, we see sin 1° to 200 decimal places:

Sin of 1 degree
Sin of 1° to 200 decimal places

See the IntMath Blog article, How do you find exact values for the sine of all angles? by Murray Bourne, 23 Jun 2011.

About five pages down, there is a link to the table of exact values of sin 1° to sin 90° by James T. Parent.

Incredible — Ed.

Bob Backstrom
~ Newsletter Editor ~

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