Sunflowers

Mathematical model of floret arrangement

Illustration of Vogel's model for n=1 ... 500
A model for the pattern of florets in the head of a sunflower was proposed by H. Vogel in 1979. This is expressed in polar coordinates where θ is the angle, r is the radius or distance from the center, and n is the index number of the floret and c is a constant scaling factor. It is a form of Fermat's spiral. The angle 137.5° is related to the golden ratio (55/144 of a circular angle, where 55 and 144 are Fibonacci numbers) and gives a close packing of florets. This model has been used to produce computer graphics representations of sunflowers.

Lily Mae

I know I should try to go in order, but since I have these pictures that I adore that I just took Saturday, I thought I'd share now.  Allie and Lily came over for a cookout on Saturday and were here for an entire 10 hours.  I took just 56 pictures... and thought I would share a few of those here.  Along with a couple of videos.  :)

She is giggleing and cooing and flailing her arms and legs a lot.  She wants to get up and go! 

She is also blowing spit bubbles, and slobbering, and it's just so cute!  Generally speaking, I don't promote these activities in those people over 1 year old or so, but babies can get away with almost anything and look cute!

This picture is currently my desktop background: 

She thinks it is hilarious when you put her blanket over her head and pull it off.  Peek-a-boo!  :)  It also makes it look like all her hair is combed forward, so I make it a point to fix it after we're done. 

And there's that adorable dimple!  She can have the most serious look on her face, and then instantly she breaks into a grin and her whole face lights up. 

She was making the funniest faces at me - I wish I would have taken video of it, but I had put my camera down and didn't want to leave her to go get it. 

Here are a couple of videos for your viewing pleasure: 

Family Sundays

Today we went to my aunt and uncle's farm to celebrate my cousin's 16th birthday.  It's amazing how peaceful it is there, how you can forget all about any problems or concerns you are having.  They have a new ATV - I forget the name of it, starts with a K, but it's like a golf cart on steroids.  I think it is this one.  My aunt Maggie took me for a ride back in the fields, and we had so much fun.  She is fearless!  We made our own paths in some spots, going over bumps so fast we both were bounced off the seat.  We also ran into a lot of tree branches that were smacking us in the face a bit.  It was so much fun. 

When we returned to the house, I took Jeff on a ride to show him the pumpkin field they had going.  Jeff was having major garden envy over there since they have a HUGE garden in addition to their 250 acres of crops.  Their tomato plants were about as tall as we are.  Sadly, they didn't plant any corn this year.  All soybeans.  :( 

It was a beautiful August day, a little cool for swimming in the lake, but when did that ever stop little boys?  Conor, Shane, and Grant all got in.  They didn't stay in too long and ended up playing in the sand because they got cold. 

Sundays with my family are always great, and this one was no exception.  :)  Of course I didn't take my camera, but I will next time. 

Catching Up: The Baby Shower

Debbie (Jon's mom, my co-grandma) and I decided to throw one big baby shower for Allie and Jon.  Cheryl (Jon's aunt) secured the location for us - her church party room.  I made this punch but used strawberry drink mix to have pink for the whole "it's a girl" theme.  :)  It was really good! 

It was a great way to meet each other's families.  We had help from our family members as well:  contributing food, drinks, help with set-up, help with clean-up. 

We shopped together for all of the supplies and food. 

We had a great turn out, too.  It was co-ed, but only 3 adult males came.  Jon's dad, Jon, and Jeff.  Conor was there too, of course.

Everything went very smoothly - we had way too much food (after not thinking we'd have enough!), we played a few games, and Lily got a lot of cute stuff.  The collective "awwww" after each gift was opened became a source of amusement for some.  There are some very talented people in our families as well, she received several hand made items - which I absolutely love.  Blankets, afghans... even some clothes!  Which, of course, I don't have pictures of yet.  Waiting months to do posts leaves you with the "where did I put those pictures?!" syndrome.  Also, don't want to overload the posts with too many pictures.  I'll have to upload them to my flickr account for your viewing pleasure at some point.  I will surely let you know when I do! 

Block Party

Banana Tree