Need A Zero

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(C)Copyright 2011, C. Burke. All rights reserved.


The best part about searching for images of 'zeta graph' is all the hits for pictures of Caterine Zeta Jones.

Ken-Do #5: Reflections of a Math Teacher

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(C)Copyright 2011, C. Burke. All rights reserved.


Remember: Sometimes it isn't the world that's upside-down.

As you might have guessed, work on the comic has slowed considerably due to
numerous factors from work and at home, which drain the creativity from me.

Lunacon and my Irish/Klingon T-Shirt

So I was at Lunacon 2011 at Rye, NY this past weekend. Happening right after St. Patrick's Day, I brought a couple of T-shirts, which I had bought at the Great Irish Fair at Coney Island last summer.

One of them had a Celtic knot similar to the Triquetra, only more knotted, with the following written across it: I Swear to Drunk, I'm Not God.

Amusing as that is to me, I did get a couple of double-takes from passersby because I'm thinking that they, in a possibly sleep-depraved state, saw a Klingon symbol before seeing it for what it truly was.

And speaking of funny looks, I got a kick out of something that happened on Saturday morning. I got my first official "I'm Not Sure if I Know You, So I'm Just Gonna Nod" nod. I'm usually on the other end of that nod after trying to start conversations with people whom it turned out I hadn't actually met over the last 25, er 15 years we've both been attending.

Triquetra -- St. Patrick's Day 2011

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(C)Copyright 2011, C. Burke. All rights reserved.


St. Patrick was a Klingon -- That would be a great meme to start!

Happy St. Patrick's Day. Go Green! But not with your food or beverages!
Don't drink any green beer or eat any green bagels!

As you might have guessed, work on the comic has slowed considerably due to
numerous factors from work and at home, which drain the creativity from me.

You Can Stop Wondering...

In case you were still wondering . . .


So now we know.



Is this an "official" comic or just a bonus?
I don't know yet.

On the March (15th)

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(C)Copyright 2011, C. Burke. All rights reserved.


The i's have it.

As you might have guessed, work on the comic has slowed considerably due to
numerous factors from work and at home, which drain the creativity from me.

Happy Pi Day, 2011!

Just wanted to take a moment to wish everyone a Happy Pi Day.
Pi is Good. Pi is Life.
We should all study The Tao of Pi.


Accept no substitutions,
except for, maybe 3.14 or 22/7, whenever more than two digits of precision aren't necessary.

And if I don't get a comic printed by 11:59pm, enjoy this Blast from the Past.

Update: When I wrote this, I didn't realize (although I should have) that there actually are websites out there called The Tao of Pi. What I wrote was meant as a joke and not an endorsement of any of these sites or products.

If anything I was using Tao to make fun of Tau. You can look it up.

Pythagorean Triples: Rides Again!

Yes, my friends and relatives think I'm crazy, but this is what I do....

Recently, in the comments to my post Pythagorean Triples: An Easier Way, blogger Keith issued a friendly challenge involving primitive triples with the same hypotenuse.

I have to be honest here: it never occurred to me that two primitive triples would have the same hypotenuse for two reasons: first, I hadn't really looked at numbers that went that high (and I'm certainly not using them in class); second, they didn't fit my three models for Pythagorean Triples: a, b, b+1; a, b, b+2; and a, a+1, c.

I explained why b+3 didn't work, but I never pondered if b+9 or b+18 would work. And, I know now, it would have.

Basically, I wanted to investigate this myself, just for fun. So I didn't use the formulas I knew about, namely pick an m and n and calculate a=m²-n², b=2mn, and c=m²+n².

That will give you every triple there is, primitive or not, with lots of repeats, in a very disorganized manner. (For one thing, b will always be the even number, not the middle number.)

But since I didn't use it, and despite the graphic I generated in this comic, I omitted the following triples from my original list of Pythagorean Triples (3-50):
33, 56, 65 and 36, 77, 85

This, of course, got me to wondering why some hypotenuses would have more than one. Well, that's kind of obvious, depending on whose lists of numbers you look at. But, of course, I'm more interested in seeing if there's any pattern to be found.

In the meantime, here's an updated list:
Pythagorean triples, sorted by the shortest side, from 3 to 50.

Leg	Primitive	Non-Primitive
3	3,4,5	--
4	--	--
5	5,12,13	--
6	--	6,8,10
7	7,24,25	--
8	8,15,17	--
9	9,40,41	9,12,15
10	--	10,24,26
11	11,60,61	--
12	12,35,37	12,16,20
13	13,84,85	--
14	--	14,48,50
15	15,112,113	15,20,25; 15,36,39
16	16,63,65	16,30,34
17	17,144,145	--
18	--	18,24,30; 18,80,82
19	19,180,181	--
20	20,99,101; 20,21,29	20,48,52
21	21,220,221	21,28,35; 21,72,75
22	--	22,120,122
23	23,264,265	--
24	24,143,145	24,32,40; 24,45,51; 24,70,74
25	25,312,313	25,60,65
26	--	26,168,170
27	27,364,365	27,36,45; 27,120,123
28	28,195,197	28,96,100
29	29,420,421	--
30	--	30,40,50; 30,72,78; 30,224,226
31	31,480,481	--
32	32,255,257	32,60,68; 32,126,130
33	33,56,65; 33,544,545	33,44,55; 33,180,183
34	--	34,288,290
35	35,612,613	35,84,91; 35,120,125
36	36,77,85; 36,323,325	36,48,60; 36,160,164; 36,105,111
37	37,684,685	--
38	--	38,360,362
39	39,760,761	39,42,65; 39,252,255
40	40,399,401	40,96,104; 40,75,85; 40,198,202; 40,42,58
41	41,840,841	--
42	--	42,56,70; 42,144,150
43	43,924,925	--
44	44,483,485	44,240,244
45	45,1012,1013	45,60,75; 45,108,117; 45,200,205;45,336,339
46	--	46,528,530
47	47,1104,1105	--
48	48,575,577	48,64,80; 48,90,102; 48,140,148;48,286,290
49	49,1200,1201	49,168,175
50	--	50,120,130; 50,624,626

PC Cliches

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(C)Copyright 2011, C. Burke. All rights reserved.


Or even "Thus, serving two scoops with one cone."

As you might have guessed, work on the comic has slowed considerably due to
numerous factors from work and at home, which drain the creativity from me.

Painting

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(C)Copyright 2011, C. Burke. All rights reserved.


And you can get electronic prints of your portrait in your choice of 5 by 7 or 8 by 10.

More on the four-color process.

As you might have guessed, work on the comic has slowed considerably due to
numerous factors from work and at home, which drain the creativity from me.

Coplanar

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(C)Copyright 2011, C. Burke. All rights reserved.


It's as plane as day.