Please Note: This page is a working document. If you use this lessons plan, please provide feedback so each lesson can be improved. There are four initial lesson plans. Additionally, curriculum will be developed for middle school and elementary school so students begin to use the models of the five platonic solids and to begin identifying the simplest tilings. All the curriculum will study constructions, tessellations and tilings, and imperfect geometries.
Organization: This lesson is designed to be 40-minutes long with an open question-and-answer period at the end. With every teaching point, you can obviously opt to go further in depth.
Background and History: Big Board-little universe came out of a high school geometry class in December 2011. It was the first universe view based on the Planck Units, base-2 exponential notation, the tiling and tessellations of the platonic solids, and simple logic.
1. What are the five platonic solids? The tetrahedron, octahedron, hexahedron, dodecahedron and icosahedron. What is a hedron (in Greek – face)? What are the other root words? Circulate the objects. There should be one per desk. If not, share. What do you have? Whose is the most simple?
2. Embedded or nesting or combinatorial geometries. Who has a figure with something inside? What is the figure? What is inside? How do they fit inside? …perfectly or imperfectly? Why?
Who has the octahedron? What is inside? Is it the simplest construction of what is inside?
b. Multiply by 2: How many times can you multiply this object by 2? (holding a tetrahedron)
Turn to the Big Board-little universe: http://SmallBusinessSchool.org/page2870.html
3. Ten steps to go over 201: Take a little tour: http://SmallBusinessSchool.org/page2990.html
4, Conclusions: Ten students read the ten paragraphs:
- Smallest to the largest, multiplying and dividing by 2, and the five, simple, platonic models
- Where are we in the textbook, “Geometry” by Bass, Charles, Johnson and Kennedy, Prentice Hall, 2004? How many references to tetrahedron in the Index? None. …to the Octahedron? 1 …to the Icosahedron? None. How about for “Real World Connections”?” Over 200. What is wrong with this picture?
More key questions:
1. Is base-2 exponential notation a useful tool for ordering information?
2. Is it meaningful to go out to the edges of the observable universe in just over 201 steps?
3. Is it useful to see the universe as a mathematical-and-geometrical whole?
4. Can we begin to grasp the concept of the Planck Length? It is so small.
5. What metaphors can we use to understand life, God, and academics?
1. Smallest: Starting points: Today, science generally accepts that the smallest possible measurement in the universe is the Planck length. Notice that is the first step on the big board. Just a single point of a very unique sort.
2. Largest: Over here in the right column is the largest measurement in the universe, it goes from one side of the universe to the other. Called the Observable Universe, it is the very last step.
3. And Everything In Between: Now let us go to the top of the board. On the left at step 101 we are at the thickness of human hair. Just under it, twice as small, is the diameter of a sperm cell. On the right at 102 is the thickness of a typical piece of paper. Just under it, twice as large, is the human egg. On what step do we find the diameter of a proton? On which step diameter of the sun?
4. Multiplication y 2. Introduce the genetic strain represented within a family. If possible use the apron, “We are Family.” The students simply multiply themselves by 2 to get 2, their Mom and Dad. Multiply them by 2 – their four grandparents. Multiply them by 2- their eight great grandparents. Assume twenty years per generation and ask the question, “How many unique women would be in their gene pool in the year 1333? In just 34 generations, going back just 680 years, we each have 16,668,545,984 Great-Greats, of which 7 billion are women usually with a different last name.
After some analysis, our simple conclusion was: Like it or not, we are family.”
The key point: In just 34 notations or steps or doublings or layers, we have billions of people in our life to make us who we are.
The universe has over 201 notations, layers, steps or doublings to make it what it is.
Size. “To begin to grasp the very-very small size of the Planck length, let us study the concept of notations. Notice that the Planck Length is 1.616199×10-35 meters. That could be written like this (a space has been added after every three zeroes): .000 000 000 000 000 000 000 000 000 000 000 01616199 meters.
Notice the edge of the observable universe is 1.038875326×1026 meters. That could be written: 103,887,532,600,000,000,000,000,000 meters.
Just by multiplying the very smallest by 2, that Planck Length, and then each result by 2, 201+ times, you are out at the edges of the Observable Universe. Not that is truly a joyous cosmology (and, this is the end of lesson 1). Thank you. -Bruce Camber
When we first developed the board for a class in December 2011, it seemed so straightforward, but we couldn’t find it anywhere on the web. That raised a few red flags. “What are we doing? Where is the logic flaw?” I pulled up the emergency brake and asked around the smarter ones in the family. A friend’s son, Robert (at Oxford following his Mom), didn’t know what to do with it. Most did not. Then, into the first round of old professor friends (like, I mean, they are really old now), they did not give us strong encouragement or discouragement. Then, to get it out in the public, Wikipedia just blew it out within four weeks . Yet, they couldn’t disagree that “The numbers are the numbers. “It wasn’t until I started corresponding with Frank Wilczek (MIT), an expert on the Planck Length, did we feel encouraged at all. That’s the history.
Today, I am working with the software company, Mathematica, to attempt to get the second lesson in shape. We will start with the point and review the Planck Length, double it (possibly a very,very short line), double it again, until we get to the 10th notation with its 1024 points. Each step we will generate more and more geometry. By end of Lesson 3, we will have gone out to the 60th step with its quintillion primary vertices and at that point I am hoping to get my old CERN friends involved and a much wider discussion about the meaning of it all.
Notes for the next three lesson plan:
1. Add Frank Wilczek’s work
2. Add continuity, symmetry, harmony
3. Add a more robust understanding of parameters.
Editor’s note: “Working article” means “always in process.”
• Basics: How’d they get here?
• Beginnings: Did a Quiet Expansion precede a Big Bang?
• Ethics-Morals-Values: Is there an inherent Goodness
within Science, Business, and Religion?
• Finite or Infinite: Is That The Question? Part II
• Paradigm Shift: Most-simple, integrated UniverseView
• Planck: Length-Time Chart All Five Basic Units Chart
• Simplicity: Everything Starts Most Simply…
• Tiling and Tessellating the Universe
• Who, What, When, Where and Why:
What’s happening here?
Take a tour of the Big Board-little universe
and its Universe Table: A short introduction
#1: The Planck Length
#2: The Range or Scale of the Universe
#3: Just by the width of a hair
#4: Discover your child within
#5: From caveats to mea culpa
#6: Water, water everywhere
#7: Transition to the Human Scale
#8: An Unknown Section of the Universe
#9: Transition to the Large Scale Universe
#10: The Observable Universe
• A Wiki-like Overview
• Our first page about this process in 2011
• Simple concept, simple beginnings
• Extremely small and extremely large numbers
• First principles & the concept of perfection
• Building Bridges