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Monday, April 18, 2005

Spiral Prompt

Blogging Prompt
Isn't this a beautiful picture? It's a picture of a giant sea shell in the Phuket Seashell Museum in Thailand. Have you ever seen this type of spiral shape before? It pops up in many places in nature. It's called a "Logarithmic Spiral." A successful response to this Blogging Prompt (you will earn your blogging mark) will answer ALL of these questions:

  1. What is a logarithmic spiral? Write it in your own words, don't copy and paste. ;-)
  2. What does it have to do with logarithms? i.e. Why is it called a Logarithmic Spiral? (Hint: Find out how it is different from an "Archimedian Spiral." Knowing what exponential functions have to do with it will help too.)
  3. Find a picture, not of a seashell, that illustrates a logarithmic spiral in nature. Post it with your reply.

Have fun with this one!

8 Comments:

At 4/19/2005 12:53 AM, Blogger Adrien G said...

Well from what i have read a logaritmic spiral also known as a growth spiral. Is a point in which a line begins and starts extending in a circular motion increasing its radius as it goes around itself. Its never crosses its own path and it may go on forever in either an outward or inward spiral.
Think of it as a cone from the top view.
the only thing about a true logarithmic spiral that makes it impossible in nature is that it is completly in unisin . I mean that there is a gradual growth to it that follows a growing pattern such as 2,4,8,16,32....

 
At 4/19/2005 1:43 AM, Blogger Adrien G said...

Well here is my stab at question 2.
a logarythmic spiral deals with logarithims in the realationshsip formed with the radius and theta of the outward spiral. That relationship can be expressed as a logarithm. That is how it got its name.

a logarithmic spiral can be creted by making a coridinate plane and drawing a ctrait line out at every 45 degrees. Then making a perpindicular line at each 45 degree interval to the next interval starting at the center to creat the spiral.

Also it differs from Archimedian Spiral in that it does not have an ewual distance between each spiral.
Oh and if you set k to 0 in a logarithmic spiral you get a circle. i'm not sure exactly what k is but this can be compared to how you cant have a logarithm with a base of 0.

 
At 4/19/2005 2:05 AM, Blogger Adrien G said...

heres a few pictures

http://www.vipgrafx.com/hippy/images/wp-sunflower.jpg


http://www.wisdomportal.com/Geometry/UrsaMajor.jpg


the double helix DNA module follows these laws of nature
and even the growth rate of rabbits as long as they never die.


This is also how Descartes thought the planets moved around the earth later disproved by who i cant remember (never did that well in physics).

Thre are many more and we use this in man made structures all the time.

 
At 4/19/2005 2:21 AM, Blogger Adrien G said...

i give up i cant get pictures to work in here for whatever reason so just copy and past the links to see the pictures.

one is of a sunflower and the other is of the milky way

 
At 4/20/2005 10:39 PM, Blogger blogster_gherard™ said...

I didn't make any research about the logarithm spiral. All I know was logarithm is an EXPONENT (and i've heard that sooo many times ^_^)....and judging the pictire, I conclude that when the spiral hits its first 360 degree revolution, its diameter will garually increse by the time the spiral hits it 2nd complete turn, and the 3rd time, it will be a lot more bigger and by the 4th revolution, the diameter will increase waay too fast, just like how exponents do to numbers. And the spiral is spinning towards infinity, but will never reach it. And the inside spiral will never reach a point where the diameter is infinitely small, in other words, it will be smaller and smaller but it will never reach zero, and that what the graph of exponential functions tell us.

 
At 4/20/2005 11:19 PM, Blogger Mr. Kuropatwa said...

Way to go Gherard! Great insight! Don't stop now .... maybe doing some research on google will help ....

 
At 4/22/2005 10:51 AM, Anonymous Anonymous said...

wow this is my first time on the blog and i think am starting to get a hang of it....
so to answer the blogging prompt i would say that a logarithmic spiral is a growth that increases by equal amounts, same ratio.it somewhat starts small and ends big and if you were to follow it you'd cover an infinite distance.
it also differs with the archimedean spiral in that its the same through out.its winding is constant.
check out some cool logarithimc shells here....
http://www.notam02.no/~oyvindha/loga.html
hows that for a first blog???!!!!

 
At 4/22/2005 11:38 AM, Blogger Mr. Kuropatwa said...

That's a great start! Two things, I need to know your name (first name only please) to credit your work, and you're very close to getting the blogging mark for answering this prompt. You just need to do two more things:

(1) Explain what this has to do with logarithms, and
(2) post a picture that is not a sea shell. ;-)

Don't stop now .... you're sooo close to your first blogging mark!

 

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