Saw this outside the house a few minutes ago.
Random rainbow trivia: the ancient Greeks believed that the goddess Iris acted as a messenger to the gods and would travel along a rainbow to deliver her messages. I assume that tradition got passed on to the Romans because even today the Spanish word for rainbow is arco iris — Iris’ arch.
Not often that I get to bust that little tidbit out.
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P.S. If you haven’t seen the double rainbow video yet, go here. It’s so intense!
A lot of people here in Central Texas believe we have only two seasons: Summer and Not Summer. It does feel that way.
This morning the temperature dipped below 70 for the first time in months, and I overheard a little boy outside my children’s school complaining to his mother about the cold. He wanted a jacket. It’ll be 85 by afternoon, though, so he’ll be okay. We won’t be hanging out in the high 60′s until sometime in November.
Now that I have a garden I realize that we do have four seasons here. You just have to be paying attention.
Do you remember Byeya’s irises in the Spring?
Here’s the same bed now, completely swallowed in lantana. I can’t even see the irises they’re so buried.
It’s a symbiotic relationship because the irises hate full sun, the lantana loves it, and during the summer the lantana provides shade for the irises. Look how it has taken over to the point of encroaching on the path. Three months from now the lantana will be dead woody stalks.
Speaking of dead woody stalks, check out the yucca:
In Spring it sends up a green stalk from its center and flowers at the top. Now the stalk is dead. I’ll snap it off when I dead-head everything at the end of Winter.
The end of Summer is blooming time for Mexican heather:
I love purple flowers. This year I’ve noticed some new wildflowers I haven’t seen before:
I wish I knew how to photograph them to do them justice. They’re very ethereal looking, like fairy tutus. I know that sounds stupid, but that’s what I thought of when I spotted them this morning. There’s a very airy, gauzy look to them. Here’s a close-up:
The fine little hairs make me think of ears.
The Copper Canyon daisy is taking over its bed like it does at this time of year. It’s the green plant in the upper right of the picture. By Halloween it will be completely covered in yellow flowers and about twice as big as it is now. Those little bushes will be buried underneath.
The dwarf nandina are telling me that Summer is ending. They are starting to turn red.
The holly berries are on the bushes, although they’re still green.
I’m sorry to tell you that I can’t remember the name of the plant in the foreground with its wonderful red blooms.
Oh, hello. I didn’t see you there.
My arthritic, bushy little live oak is producing acorns.
This little flowering annual whose name I’ve forgotten loves its location in front of the patio. Behind it is the overturned inflatable kiddie pool. If that isn’t a sign that summer is ending, I don’t know what is.
My wild lantana wants to put up an argument. “Look! There’s still a hammock up!” it says.
Right next to it, however, the redbud is losing its leaves.
It may still feel like Summer, but the plants are telling us that Fall is on the way.
I like carbonated fruit sodas. I like them in glass bottles.
Hardly any sodas come in glass bottles anymore, and it’s a shame. Glass is a wonderful insulator. The soda comes out of the fridge so cold it has extra bite.
These particular glass bottles have the added attraction of a very cool flip top.
You pull the wire forward, and *pop* goes the ceramic stopper. (It has a rubber ring around the bottom to give it a better seal.) Somehow soda tastes better when you have audio anticipation.
The labels on these particular sodas are kind of homely. I can see they’re reaching for a feel of Renoir or maybe a vintage French poster, but all I’m seeing is a bunch of discordant colors and images vomited onto a label.
Not that that stops me from enjoying my soda. My current favorite is pink lemonade.
Underneath the labels, these bottles are beautiful. I realized quickly that it would be a shame to toss them into the recycling bin.
The Big M and I visited a little French country restaurant in Seattle that brought out bottled water to the table. Looking at my soda bottles, I thought it would be fun to do the same.
So I soaked the bottle I had on hand in hot, soapy dishwater, and then peeled off all the labels. Then I filled it with tap water and stuck it in the fridge to chill.
Isn’t that pretty? Makes you want to drink water, doesn’t it?
The bottle itself has additional beauty that is easily overlooked with all those labels distracting you.
I love the knobby glass texture under my fingers, all cold and sweating. The visual is nice, too. It’s the kind of glass bottle you’d have to pay $10 or more for at a retail outlet, but I got it for $3 at a grocery store. And it came filled with soda.
We stick a bottle on the table at suppertime and call it our “Fancy French Water.” The kids think it’s fun. I do, too.
Jeannette McCurdy was a checkered garter snake. She lived in our backyard until this morning, when she was discovered deceased on the neighbor’s driveway.
Before her untimely demise, Jeannette looked something like this:
She was a lovely little snake, with a nice yellow stripe down the middle of her back. She was about 10 inches long. We don’t think she made it to full adulthood.
My children gathered with their neighbors (also 8 and 6) to put Jeannette to rest. First, they determined she was a girl. Then they named her. Then they chose a resting place in a flowerbed. Then, while wailing loudly, they gathered flowers and other decorations to mark her gravesite.
Finally, they added a headstone with her initials on it:
After that, they went inside to eat and visit, which is what one always does after a funeral.
Rest in peace, our reptilian friend.
Every now and then I put in the DVD for a lecture series on discrete mathematics and watch one. I like discrete math because a) it’s not calculus and b) it’s all about patterns, so it’s like doing a puzzle. I can actually wrap my head around discrete math. It suits the regimented side of me.
Anyway, today’s lecture started off about recognizing patterns in series of numbers added together. I knew (half my life ago) that there was a shortcut, but I never knew what it was or even thought about it after high school.
Professor Arthur Benjamin* showed an example series. Say you want to add up consecutive odd numbers starting with one. What’s a quick way to determine the sum without physically adding them all? You try to find the pattern.
1=1
1+3=4
1+3+5=9
1+3+5+7=16
1+3+5+7+9=25
and so forth.
If you were to assign the number n to mean the number of numbers (sorry if that’s confusing) in the series, you’d start to see a pattern:
if n=1, then the series is 1=1, which is the same as 1=1²
if n=2, the series is 1+3=4, which is the same as 1+3=2²
if n=3, the series is 1+3+5=9, which is the same as 1+3+5=3²
and so on. So we figure out that if we add together n consecutive odd numbers starting with one, the sum will be n².
Let’s say we have the series:
1+3+5+7+9+11+13+15+17+19+21
We can count all the numbers, and we see there are 11. Eleven squared is 121, so the sum of that series is 121.
But what if you have a series that’s super long, and you don’t want to count how many numbers are in it? You find the pattern for the last number in the series and how it relates to n.
Again, the series:
for 1 , n = 1
for 1+3, n = 2
for 1+3+5, n = 3
for 1+3+5+7, n = 4
so,
when n = 1, the last number in the series is 1
when n = 2, the last number is 3
when n = 3, the last number is 5
and when n = 4, the last number is 7
If we puzzle it out, we’ll notice that by doubling n and subtracting 1, we’ll get that last number. So, for example, when n = 4, we get the last number, 7, by doubling 4 to make 8 and subtracting 1. The last number is 2n-1.
So now we can write the series this way:
1+3+5+7+…+(2n-1)=n²
I now have the shortcut. If I want to know what the sum of all odd numbers up to 99 are, I don’t have to write them out. I can say, “I know the last number is 99, so 2n-1 is 99. I can add one to make 100, divide it by 2 to get 50, and now I know n is 50. So the sum is 50 squared, which is 2500.”
I determined to figure out on my own the pattern for summing consecutive even numbers starting with 2, and in about 15 minutes of drawing it out, I did it! The answer is:
2+4+6+8+…+2n=n(n+1)
If I want to know the sum of all even numbers up to 100, I know that n=50, which makes the sum 50 times 51, or 2550.
I’ve never figured out a mathematical pattern by myself before, so I just wanted to share. It was kind of exciting!
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*Arthur Benjamin is a wonderfully enthusiastic teacher. You can check out his “Mathemagician” web page here.
