Monday, January 24, 2022

How not to communicate one's GPS location

Alas, Apple has made the ad unavailable. "The owner of this Apple Watch has taken a hard fall and is not responding to their watch. The emergency location is latitude 47.7, longitude -117.5, with an estimated search radius of forty-one metres."

Bob B. (presumably no relation to the unfortunate Amanda A. [video ad also now unavailable] who flipped her car in fast-rising, muddy water) was knocked unconscious mountain biking in a forest just west of Spokane WA with his watch supposedly making the 911 call. No doubt countless targets of the advertisement will ask Google Maps for the location of the coordinates:
Wow! Exactly on a bicycle-friendly road in a wooded area. But there is something amiss. To achieve such pin-point accuracy one needs precision somewhat beyond the given tenths of a degree latitude/longitude. 47.7000 N, 117.5000 W would do it, although the 41-metre search radius suggests 47.700 N, 117.500 W is probably sufficient. A GPS location is likely given in degrees/minutes/seconds (not decimal degrees) and this would have the desired accuracy. I am not acquainted with the Apple Watch emergency-call GPS specifics but I will point out that by approximating the location as 47.7 N, 117.5 W (dropping the terminal zeros), it implies an error box of ~7.5 km east-west and ~11.1 km north-south. That's a search-area of over 8300 hectares! Poor Bob.
47.7º N, 117.5º W, approximation error box (in magenta), click to enlarge

Friday, January 21, 2022

Telephone puzzler

Local calls appeared to be getting through on our home-phone landline but not long-distance calls, as evidenced by a handful of instances over the course of a month. I was certain that the problem lay in some distant Bell relay device and that the technician likely wouldn't have to come into the house. I was wrong.

Ekene, technician, connecting a new cable to a nearby Bell hub

Monday, January 17, 2022

Snow

Early this morning, coming home after the dog-walk. Twelve hours later we had ~40 cm.

Tuesday, December 21, 2021

Wildlife

coyote under the streetlight, click to enlarge
Spotted walking from Clouston Avenue through Denison Park on this morning's dogwalk, a furtive coyote has just left the north end of park and is about to walk up Denison Road West. I managed to get a lot closer to a fox that I saw on Sykes Avenue back on November 27:

Thursday, December 16, 2021

YYZ


From high above my abode in south Weston, courtesy the latest version of Mathematica, a graphic representation of Canadian and U.S. flight paths yesterday that started or ended at nearby Toronto Pearson International Airport. Zooming in ...



Sunday, December 05, 2021

Weston Station

click to enlarge
In the above Toronto transit map, Weston Station is clearly marked on the UP Express and GO Line Service routes, heading northwest out of (downtown) Toronto. As one might expect, it is just south of the extended horizontal line connecting Lawrence West (University, line 1) and Lawrence (Yonge, line 1) subway stations.

Roy Murray wrote an article on WestonWeb.ca about Castlepoint's "Weston Park" proposed development right beside Weston Station, pointing us to a YouTube video by Castlepoint Numa on the project. I watched it on December 2nd and noticed that the location of Weston Station had been moved southeast so as to appear much closer to Eglinton Ave. W. in Mount Dennis. So I decided to make a YouTube comment pointing that out: "There's a transit map at 0:50 to 0:55 where Weston Station pops up at an incorrect location. It's actually a good deal further northwest. Presumably the disingenuous placement is meant to convince the target of this propaganda piece of the station's proximity to the Eglinton Crosstown corridor."

click to enlarge
I noticed today that my comment had been removed and comments turned off.

Thursday, November 18, 2021

Pandigital palindromic sums

Two days ago Éric Angelini posted on MathFun:

234567898765432 + 1000000000000000 = 1234567898765432

... noting that (ignoring the arithmetic symbols) the concatenated 47 digits are a palindrome. Éric wondered about smaller palindromic sums where all ten digits are present ("pandigital" in the sense of A171102). Here are the 24 smallest:

12076 + 38354945 = 38367021
12076 + 83854945 = 83867021
12376 + 80854945 = 80867321
12876 + 30354945 = 30367821
13086 + 27254945 = 27268031
13086 + 72754945 = 72768031
13286 + 70754945 = 70768231
13786 + 20254945 = 20268731
21067 + 38354945 = 38376012
21067 + 83854945 = 83876012
21367 + 80854945 = 80876312
21867 + 30354945 = 30376812
23087 + 16154945 = 16178032
23087 + 61654945 = 61678032
23187 + 60654945 = 60678132
23687 + 10154945 = 10178632
31068 + 27254945 = 27286013
31068 + 72754945 = 72786013
31268 + 70754945 = 70786213
31768 + 20254945 = 20286713
32078 + 16154945 = 16187023
32078 + 61654945 = 61687023
32178 + 60654945 = 60687123
32678 + 10154945 = 10187623

Thursday, November 11, 2021

What a difference five months make

Five months ago, I showcased the then-ten-largest-known Leyland primes. Here's an update:

500973  (100207,99856)   Gabor Levai          Nov 2021
500702  (100263,98600)   Gabor Levai          Sep 2021
386642   (81650,54369)   Yusuf AttarBashi     Jun 2021
386561   (80565,62824)   Hans Havermann       Aug 2021
386548   (83747,41272)   Hans Havermann       Aug 2021
386434  (328574,15)      Sergey Batalov       May 2014
302858   (84181,3960)    Hans Havermann       Nov 2021
301815   (83278,4209)    Hans Havermann       Sep 2021
301763   (64431,48250)   Hans Havermann       Sep 2021
301716   (67237,30714)   Hans Havermann       Sep 2021

The first column gives the number of decimal digits. The Leyland number of an (x,y) pair is x^y + y^x. Nine of these ten entries are new. Of course my list of all known Leyland primes is always up-to-date.