The Mandelbrot Set

 FRACTALS:

 wikipedia:
Benoit B. Mandelbrot ^{[note 1][note 2]} (20 November 1924 – 14 October 2010) was a Polish-born, French and American mathematician, noted for developing a "theory of roughness" in nature and the field of fractal geometry to help prove it, which included coining the word "fractal". He later created the Mandelbrot set of intricate, never-ending fractal shapes, named in his honor.^[6]  

He said that things typically considered to be "rough", a "mess" or "chaotic", like clouds or shorelines, actually had a "degree of order".^[7]





http://www.ddewey.net/mandelbrot/

School Today: Fibonaaci, Plants, Geometry, Drawing

Our dining table loaded with the days inspiration.

Drawing the Fibonacci Sequence on graph paper to create spirals.

The Fibonacci numbers: 0,1,1,2,3,5,8,13,21,34,55,89, etc.

This flower has 3, 5, 13 (there are 3 green petals in the back that you can't see)

Strawberry leaves- in 3's.

Specialized pollen position perfectly suited for the large black bee that frequents the vine.

Da Vinci's Vitruvian Man 1490 AD

We put this to the test by comparing our own measurements and proportions.

The lower section of text gives these proportions: (from Wikipedia)

• the length of the outspread arms is equal to the height of a man
• from the hairline to the bottom of the chin is one-tenth of the height of a man
• from below the chin to the top of the head is one-eighth of the height of a man
• from above the chest to the top of the head is one-sixth of the height of a man
• from above the chest to the hairline is one-seventh of the height of a man.
• the maximum width of the shoulders is a quarter of the height of a man.
• from the breasts to the top of the head is a quarter of the height of a man.
• the distance from the elbow to the tip of the hand is a quarter of the height of a man.
• the distance from the elbow to the armpit is one-eighth of the height of a man.
• the length of the hand is one-tenth of the height of a man.
• the root of the penis is at half the height of a man.
• the foot is one-seventh of the height of a man.
• from below the foot to below the knee is a quarter of the height of a man.
• from below the knee to the root of the penis is a quarter of the height of a man.
• the distances from the below the chin to the nose and the eyebrows and the hairline are equal to the ears and to one-third of the face.

Results:  Baron's arm span and height are 53' and 53' but his feet are 9' and are supposed to equal 1/7 of his height and it was 10' off.  My arm span is 3 inches short of Vitruvian's proportions and my foot at 10' and height of 67 left me short as well.  We did a few more and some were hits but others misses.  Great way to put fractions, measurement, conversions, and proportions to work in real life context! 

Fibonacci Sequence

Having investigated the helical motion of the solar system, we stumbled upon the Fibonacci Sequence as it relates to spirals.  Perfect, since we needed to do math and Baron is really resisting workbooks and worksheets today. 

First stop:
The single most interesting, fascinating, and  exciting investigation into math!!!!
Khan Academy:
This one sooooooo WONDERFUL!!!!! Thank God for Khan!!!!!!

www.khanacademy.org/math/recreational-math/vi-hart/spirals-fibonacci/v/doodling-in-math--spirals--fibonacci--and-being-a-plant--1-of-3

Less exciting but we love Sal.
https://www.khanacademy.org/science/computer-science/v/exercise---write-a-fibonacci-function


wikipedia:

Leonardo Pisano Bigollo (c. 1170 – c. 1250 AKA Fibonacci, was an Italian mathematician, considered by some "the most talented western mathematician of the Middle Ages."^[2]


"Fibonacci numbers are closely related to Lucas numbers in that they are a complementary pair of Lucas sequences. They are intimately connected with the golden ratio; for example, the closest rational approximations to the ratio are 2/1, 3/2, 5/3, 8/5, ... . Applications include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings,^[8] such as branching in trees, phyllotaxis (the arrangement of leaves on a stem), the fruit sprouts of a pineapple,^[9] the flowering of artichoke, an uncurling fern and the arrangement of a pine cone.^[10]"

 A great video illustrating the concept:

http://www.youtube.com/watch?NR=1&feature=endscreen&v=bE2EiI-UfsE

New question:  What is the Golden Ratio? 34/55

Ah, so much yet to explore!

Vortex/Vortices

 Ahhh, homeschooling and 3rd grade science.  This is where the morning took us...


Today we looked at VORTICES and did an experiment with two Pepsi bottles and a vortice junction.
Question:  What is a vortex?
Baron:  A vortex is the spinning movement that makes a tornado or whirlpool in liquid, gases, and air.  It spins and sucks everything towards its center.

Question:  Give me examples of vortices.
Baron:  Water creates a whirlpool.

Baron:  The solar system exists in a vortex.
Question:  Please expand on that thought.
Baron:  That's hard to expand on.
Please try.
Baron:  Planets spinning around the sun in a helical motion.
Question:  How do we know that the galaxy is a vortex?
Baron:  Actually, the outer space force is pulling and it keeps everything in place and the sun is pulling and gravity keeps the planets in position in the vortex.
Question:  Can you think of examples of vortices?
Baron: Hurricanes, storms, tornadoes, and Jupiter's storm.
Very good.

We watched an interesting video about the helical vs heliocentric movement in our galaxy.  A must-see in HD!
http://www.youtube.com/watch?v=C4V-ooITrws


A very straight forward explanation of the helical orbit theory.
http://www.youtube.com/watch?v=2oS2vZe-TGU

Hydroponic Farming

 

 Last Friday, we went to the http://www.temeculavalleystrawberryfarms.com for a farm tour to learn about hydroponic farming.

The Benefits of Earth Friendly Farming are Clear

• Energy Savings
• Less Water
• No Soil Borne Pests or Diseases
• Every Plant is Micro-Managed
• Higher Yields
• All Natural

Water Study

I woke the other morning to several glasses of water left unused from the day before.  We decided to measure the amount of wasted water over a period of time to generalize how much drinking water we waste on average. 

 

We tried to estimate quantities on this gallon jug, breaking it into fractional parts.  Then my mom came over disgusted by the crazy kitchen mess and poured out our water and threw away the jug.  Thank you, Mom.  I never said homeschooling was perfect!!

 

Then that whole conversation led to the next issue- emergency water supplies.  What would we do if the infrastructure failed and we had no water?  We would resort to extreme rationing and would have to seek clean water for consumption.  Baron ran out to the trunk of my car, pilfered my trunk for the bug-out-bag, got out the Kayadyn water filter and proceeded to thoroughly investigate it. 

Creative Fun

Sometimes it's just fun and games!

Baron dressed for his debut at the Thursday Group Creative Improv

Life imitating art.

Healthy Food Fun

Story Boards and Animal Tracking

Baron Goes to the TOP!!!!

Making a Switch

Fall-Brook Reche, Mrs. Dapper's Science Class

3-2-1 BLAST OFF!!!!! Rocket Launching Day

 

Niah's super hot, pink and gold, glitter rocket ready to launch during Mr. Shirley's Physical Science class last week.

A major success with high flying action!

Niah and her favorite teacher that LOVES to blow things up. 

I, Juan de Pareja

 We just finished our book.  What a wonderful story that gave life to real history.  We met famous artists of the 17th century, Ruebens, Velasquez, and Pereja.  We looked at their art as we read this historical fiction.  We learned about early Spain and its court, the Plague, Gypsies, art history, Rome, slavery, love, tragedy, character, humility and humanity.  I never realized learning about history could be so enjoyable.

Velasquez, self portrait.

Ruebens

TEST PREP Time!

Working diligently on TEST PREP for the CST.  It's a big one this year for Niah who will have Science in addition to Language Arts and Math.  It believe they will both do well but I sweetened the pot by setting an opportunity for reward by working hard during test-prep then getting through the test days.  Niah wants a Taylor Swift gift set and Baron, a hydration pack.  I know we shouldn't always reward for things they should do anyway.  However, there is nothing wrong with reward for hard work and success.   After all, don't we work hard for reward?