#Gus Lemoine

[mudwerks]

(via Fast Willie Jackson #1 - 1st appearance - Pencil Ink)

Published by Fitzgerald Periodicals, these characters were conceived as the African-American version of Archie Andrews and company. Among Willie's supporting cast were his best friend Jo-Jo, muscle-bound Hannibal Jones, popular girl Dee Dee Wilson and others. The stories were written by the publisher himself, Bertram Fitzgerald and drawn by Gus Lemoine (possibly a pseudonym for one of the regular Archie artists). Cover by Lemoine.

[jhsharman]

humble fumble, ballot boxed

Not sure what "try being popular" even means. I don't think Reggie ever wins these things.

The execution on "Ballot Boxed", where after seeing how everyone is swayed by Jughead's slogan posters for Archie's candidacy Reggie buys him off and you see the rest here, leaves something to be desired. It needs just a mite better slogans than "Archie By Cracky" for me to suspend disbelief and accept. On the soundness of the premise, I am reminded that in voting for asb positions, having nothing else to go by and no clear idea of what the heck I was voting for besides a good line for the candidates' college applications, I voted for whoever have me the most number of campaign stickers.

[cccovers]

Fast Willie Jackson #5 (June 1977) cover by Gus LeMoine and Barry Grossman.

[thesabrinatheteenagewitchblog]

And the rest!

[cryptocollectibles]

Laugh 8 Issue Lot (1972-1982) by Archie Publications

Written and drawn by various.

[squareallworthy]

Triangle Tuesday 6: More on parallels and antiparallels, wonky hexagons, and a couple of conjectures

I had a very busy weekend so I haven't been able to write up the next subject I had planned on. Instead, I'm just going to show you some neat stuff about parallels and antiparallels in a triangle and not prove any of it.

To recap, last week we saw that a special property of the symmedian point K of a triangle is that if you draw parallels to the sides through it, the points where they meet the sides lie on a circle. This is called the first Lemoine circle, and I have labeled its center as point U.

And if you draw antiparallels through K, they also all meet the sides on a circle. This is the second Lemoine circle, and its center is K.

And we can also draw circles through K and any two of the vertices. These circles intersect the extended sides at points on a common circle as well. This is a much more recent result that I learned about here, and we'll call this the third Lemoine circle, with its center at V.

What I didn't mention before is that these three points K, U, and V all lie on the same line, along with the circumcenter O.

This line that connects O and K is known as the Brocard axis. What's more, as far as I can tell, the four points are equally spaced on the Brocard axis. I haven't been able to find a reference to that, and I haven't even tried to prove the equal spacing, so we'll just call that part a conjecture.

Another line that runs through the circumcenter is the Euler line. Other famous points on this line are the centroid G and the orthocenter H.

Not so famous, but still in ways important, is the point I have labeled W, the midpoint of G and H and the center of the orthocentroidal circle. These four points O, G, W, and H are also equally spaced. And (more conjecture) the lines GU, WK, and HV are all parallel.

Again, I have not even tried to prove this, but I thought it made a curious observation and I wanted to share it.

Let's switch gears and go back to the first Lemonie circle.

The blue segments are, remember, parallel to the sides of the triangle. If we join the endpoints of these segments to their nearest neighbors on adjacent sides, we get a self-intersecting cyclic hexagon, in gray. And it turns out that the new segments we have just drawn (red) are antiparallels.

Shall we also try that with the second Lemoine circle?

Yes, we find that the new segments we've added are parallels to the sides. So in both cases we got a self-intersecting hexagon of alternating parallel and antiparallel sides.

So is this another special property of the symmedian point?

Here is a hexagon of alternating parallel and antiparallel sides that I drew starting from an arbitrary point on the bottom side of the triangle. We still get all the vertices of the hexagon landing on a circle.

And indeed this construction works if you start from any point. The symmedian point is only special in that if the three parallels or antiparallels cross at one point, that's where they do it. Hexagons like this are called Tucker hexagons, and their circumcircles are called Tucker circles.

Okay, but what if we made a hexagon like this but only using parallels?

We still get a hexagon, but the points of contact with the sides fall on an ellipse rather than a circle. When three segments meet, they do so at the centroid, and when segments overlap in pairs so that we get a triangle, it's the medial triangle. This hexagon is called Thomsen's figure, btw.

What about using only antiparallels, then?

Looks like it forms an ellipse in the same way Thomsen's figure does. I have no idea what this is called, if it has a name at all. I'm just playing around and didn't even expect it to work.

That's about all I have time for this week. Hopefully this weekend won't be so busy and I'll be back with something more focused.

If you found this interesting, please try drawing some of this stuff for yourself! You can use a compass and straightedge, or software such as Geogebra, which I used to make all my drawings. You can try it on the web here or download apps to run on your own computer here.

An index of all posts in this series is available here.

[graphicpolicy]

Preview: Archie Comics 80th Anniversary Presents Sabrina

Archie Comics 80th Anniversary Presents Sabrina preview. Meet everyone's favorite teenage witch--Sabrina! Explore how Sabrina balances her magical life with her normal teen life, including at school and in romance. #comics #comicbooks #digitalcomics

ARCHIE COMICS 80TH ANNIVERSARY PRESENTS SABRINA

Script: Various Art: Various Cover: Gus LeMoine On Sale Date: 5/13 $1.99

Meet everyone’s favorite teenage witch–Sabrina! These stories explore how Sabrina balances her magical life with her normal teen life, including at school and in romance. Plus, some very special cameos from Archie and the gang!

[dirtyriver]

...and Betty to a Shady Motel (that's its name, honest) where they get naked after pretending to be married.

Betty and Me #40, February 1972

[jhsharman]

"nice try"

[cccovers]

Fast Willie Jackson #3 (February 1977) cover by Gus LeMoine and Barry Grossman.

[thesabrinatheteenagewitchblog]

Another "Sabrina flunks at helping" story, and not a personal favourite XD but here goes! "That Ol' Black Magic" by Dick Malmgren and Gus Lemoine! Featuring the original Ethel Muggs and female Salem! A continuity error or a genuine change for a while? No idea! Also our first Harvey appearance in this book!

[blackfolksmakingcomics]

Fast Willie Jackson #1 by Gus LeMoine

I love the youthful energy of this cover.

[jhsharman]

snooze ruse, "a little sleep"

[cccovers]

Fast Willie Jackson #1 (October 1976) cover by Gus LeMoine and Barry Grossman.

[jhsharman]

Slice of pizza

We establish that Jughead carries that slicer around with him.

But Archie did it first.

[cccovers]

Fast Willie Jackson #7 (September 1977) cover by Gus LeMoine and Barry Grossman.