Hyperbolic Planes & Pseudospheres

Dear LuLu, the news about your sis is certainly disheartening. I'm thinking about you, and praying for strength for you both, and wisdom on the part of her medical team.

I've made a little progress on Sleeve #1. It's quite phenominal, the way it expands from the long cuff. (That's the cuff, the skinny tube sticking up in the middle.) The pattern calls for increasing to 180 stitches around, but I've called a halt at 120. Just look at the size of that sleeve! Don't you think that'll be enough?!

One of my favorite fiber books of the past year is "Crocheting Adventures with Hyperbolic Planes." The author, Daina Taimina, is a professor of mathematics. She crocheted examples of hyperbolic planes to demonstrate to students their properties. (Be patient -- there's a connection here.) Do you remember the definition of parallel lines, that you learned in geometry? Through a point not on a line, there is one, and only one, line that is equidistant from the first line at every point on the line. Something like that. Well...that definition works on a flat plane. But what about on a sphere? If straight lines are the shortest distance between two points, on a sphere those would be great circles. And there are NO great circles that won't intersect every other great circle on the sphere.

So what about the opposite of a sphere? If a sphere is a surface that's always closing in on itself (mathematicians say it has positive curvature), then the opposite (negative curviture) would be a surface that's constantly expanding. And guess what? On such a surface (called a hyperbolic plane), there are an infinite number of lines that will not intersect the first line.
Mathematicians (men, of course) have been trying for the several centuries since they started thinking about such things, to figure out how to SHOW such a surface and its properties. It took a woman mathematician, with a crochet hook. You could do it with knitting, but eventually you'd have too many stitches on the needle, so crochet works best. Make a chain, close it, and as you go around, increase the number of stitches in every round. That's a hyperbolic plane!

And here, dear LuLu, is the point of all this: Doesn't my KF sleeve look for all the world like the beginning of a pseudosphere, which is a special kind of hyperbolic plane?

I'm off to Central America for a few days, wearing my accounting hat, on behalf of my favorite charitable organization. I won't take the fuzzy, woolly Romeo & Juliet sleeve: it'll be in the 90s, with 95% humidity!

Signet ring cell

Buffy, my sis got her latest diagnosis yesterday, signet ring cell carcinoma of the appendix. In the 25 years between 1973 and 1998 there were only 70 reported cases of signet ring appendix cancer in the USA -- less than 3 people each year.


So it's nothing anybody does -- it's just the luck of the draw. I liken it to the short story The Lottery, where on a certain day each year all the names of the villagers are put into a hat. One is drawn out. All the villagers join in to immediately stone that person to death. All then go home and have a good life until the next lottery day.

When news is not news.

Buffy, I drove to the midwest for a few days to visit my sis. There's news. She does not have ovarian cancer; instead she has cancer of the appendix, a very rare cancer. There are less than 1000 new cases a year, as compared to colon cancer, which is diagnosed about 165,000 times. That leaves it an "orphan" cancer, and treatment centers and specialized oncologists are few--and yes, far between. Appendix cancer comes in five flavors, and it is not yet clear to her which kind she has or what the treatment will be. Although the prognosis is terrible, the numbers are so small that the charts may be skewed to the downside since newer treatments might be giving better results.

 So I will be traveling frequently this summer since she will need help with transportation to perhaps Omaha, Chicago or Indianapolis. I will knit along on the coat patches while I am at home, and take a different project with me when I travel.

I love, love, love the colors of your Juliet. What changes did you make to the stripe pattern to shorten your coat? Are you changing the sleeves?