Skip to main content

How does math relate to real life?


By Jeanne Lazzarini, Math Master Educator/R&D Specialist, RAFT

How does math relate to real life?  One way is to take a look at the shape of a cloud, a mountain, a coastline, or a tree!  You might be surprised to find that many patterns in nature, called fractals, including growth patterns, have very peculiar mathematical properties ---  even though these natural shapes are not perfect spheres, circles, cones, triangles, or even straight lines! 

3D Fractals For Inspiration

 
So, what is a fractal?  Benoit Mandelbrot (November 20, 1924 – October 14, 2010) is commonly called the father of fractals. He created the term “fractal” to describe curves, surfaces and objects that have some very peculiar properties. A fractal is a geometric shape which is both self-similar and has fractional dimension.  

Daydreaming fractals


Ok, so what does that mean?  Well, “self-similar” means that when you magnify an object, each of its smaller parts still look much the same as the larger whole part. And, “fractal dimension” is different from what we use to describe shapes such as lines, flat objects, and geometric solids.  Simple curves, such as lines, have one dimension.  Squares, rectangles, circles, polygons, etc. have two dimensions, while solid objects such as cubes and polyhedra, have three dimensions.  Some say time is the fourth dimension.  In all these cases, dimension, based on Euclidean Geometry, is described as an integer: 1, 2, 3, 4, … 
 
But a fractal curve could have a dimensionality of 1.4332, for example, rather than 1!  A fractal’s dimension indicates its degree of detail, or crinkliness and how much space it occupies between the Euclidean Geometric dimensions.  Most objects in nature aren’t formed of squares or triangles, but of more complex fractal shapes, such as ferns, flowers, coastlines, clouds, leaves, trees, mountains, blood vessels, broccoli, weather, lightening, fluid flow, river estuaries, circulatory systems, geologic activity, fault patterns, planetary orbits, animal group behavior, music, and so forth. 

Whew! By understanding fractal dimension, mathematicians can now measure forms that once were thought to be immeasurable!   


Romanesco broccoli fractals

Have fun discovering “fractals” with RAFT’s “Freaky Fractals” activity kit!  Use the kit to create a fractal shape resembling “arteries”, “coral”, “a heart”, “a brain”, “tree branches”, etc. Then go to the store, buy some broccoli or cauliflower, then take a  close look! Break off a branch and what do you see?  The smaller branch looks just like a miniature copy of the whole vegetable!  Now look around you and you’ll notice thousands of living examples of self-similarity in ferns, coastlines, clouds, leaf veins, trees, and the formation of shells, mountains, blood vessels, lightening, river estuaries, circulatory systems, fault patterns, galaxies, musical compositions, and so forth!  By understanding fractal dimension, mathematicians can now measure shapes, such as coastlines and so forth that once were thought to be immeasurable! Fractals are AWESOME!  Math really is all around you when you stop to look!

Comments

Popular posts from this blog

Are you ready for Pi?

Time to get ready fer Pi Day at RAFT me hearties!  Set yer compasses an’ sails fer FREE Pi Day activities on March 8thbetween 3:30 to 5:30 on th’ main poop deck (aye-aye in th’ “Kit Area”) at SJ RAFT!
RAFT’s very own notorious wench, Jeanne Lazzarini (RAFT Math Master Educator), prepared a boatload of Pi Day activities to share with yer classes fer Pi Day (celebrated on March 14th every year)! Pi, (also written as π; th’ ratio of th’ circumference of a circle to its diameter) be an irrational number that goes on forever without any repeating digits, starting with 3.14159… π is illustriously celebrated over land an’ high seas March 14th (get it? On 3.14…!).    Discover great “make-an’-take” Pi day activities that prepare ye fer real Pi day!  Here’s a RAFT idea sheet fer Pi Day you can use now: Pi Day Pin. Make sure X marks th’ spot on ye calendars this March 8th, or walk th’ plank me scallywags!   Shiver me timbers an’ yo-ho-ho!  ‘Tis a RAFTy life fer me, Bucko!!!  Arrrgggghhhhh!

CUSD Shares Possible STEAM Projects by Grade

Twelve STEAM Innovation Leaders from the Campbell Unified School District (CUSD) came to RAFT earlier this month to create new motivational activities for the start of the school year!  They met in grade-level teams with our RAFT Education staff to generate new ideas using RAFT materials that will motivate, challenge, and inspire their students. Each team was given a RAFT Makerspace-in-a-Box containing a wide variety of upcycled materials. They were asked to create a Design Challenge that directed students to solve the instructor’s challenge with the materials from the box. The Design Challenges addressed an engineering standard appropriate for each grade level and could include standards from other subjects. Here are some of their exciting back-to-school ideas:
************************************************************************************* Grades TK – 2 Engineering Standard: K-2-ETS1-1:  Ask questions, make observations, and gather information about a situation people want to chan…

Use the Winter Olympics to engage your students

The 2018 PyeongChang Winter Olympics are right around the corner!
This worldwide event offers excellent opportunities to use the Olympics to inspire your students to learn about many mathematical concepts such as slope. How can the Olympics help students understand slope? Think of ski slopes! Ask students to watch the Olympics this year on TV and to look for sports that use steep paths (e.g., snowboarding, downhill skiing, alpine skiing, bobsleighing, etc.)! Back in class, have students recreate replica “ski slopes” using sections of white foam board. Place one end of a foam board against a wall with the opposite end touching the floor at an angle so that it forms the hypotenuse of a right triangle (the right angle is between the wall and the floor). Refer to the vertical distance (“rise”) from the floor to where the top edge of the board touches the wall as the y-intercept. Refer to the horizontal distance (“run”) starting at the wall and to the bottom of the board farthest away from t…