12 Pentagons Make a Dodecahedron

Or 2 pentagons each having 6 smaller pentagons in it make a dodecahedron.

Polyhedron like dodecahedron will be explored with Excel to use polygon like pentagon as building blocks.

I have designed and drawn a chain of 12 pentagons to cut and fold to make a dodecahedron dice so we can play with our kids. Excel Trigonometry.

Martin Gardner Challenges us in "In the beginning God...."

"1) In the beginning God created the heaven and the Earth.

2) And the earth was without form, and void; and darkness was
upon the face of the deep.
And the Spirit of God moved upon the face of the waters.

3) And God said, Let there be light: and there was light."

In "Wonders of Numbers" (Clifford A. Pickover, 2000), Mathematician Martin Gardner challenges the reader to find out that:

Start with any word in 1) above ('In' to 'Earth'), and count the number of (length of) the word (say 3 in 'the'): "n1";

and Proceed to the word n1 after the first word (say 'created'), and count the number of (length of) the word (7): "n2";

and Proceed to the word n2 after the second word ('created'),
and so forth, and the two 'God's (one each in 2) and 3)) will thus end up just n* after the preceeding words.

My Excel spreadsheet will help find out about this.

Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning

Correct? "phi - (((1 / phi) * (1 - ((1 / phi)^70))) / (1 - (1 / phi))) = 0"

phi - (((1 / phi) * (1 - ((1 / phi)^70))) / (1 - (1 / phi))) = 0 is not verified by what I figure out with my Excel Trigonometry.


06/12/12

((1 / phi) * (1 - ((1 / phi)^70))) / (1 - (1 / phi)) = 1.61803399, more precisely, means that:

1. 1/phi + 1/phi^2 + 1/phi^3 + .... + 1/phi^70 is 1.618033988..
   


2. 1/phi + 1/phi^2 + 1/phi^3 + .... + 1/phi^70 + .... + 1/phi^n
   becomes indefinately closer to phi as 'n' increases to infinity.
   
   Phi to 20,000 places

Note:

1. 1/phi, 1/phi^2, 1/phi^3, ... forms Fibonacci Numbers


2. Formula for the geometrical series for this:
   (((1 / phi) * (1 - ((1 / phi)^n))) / (1 - (1 / phi)))


3. phi+1, (phi+1)^2, (phi+1)^3, ... also forms Fibonacci Numbers

Try Exploring Vector in Hexagon and Heptagon with Excel

Try exploring Vector in Hexagon and Heptagon with Excel.
Excel Vector Trigonometry is launched today to show how to use Excel to make calculation for vectors with trigonometry.
- November 26, 2006 -

06/12/14
"<-0.5: The minimum inner product with T, O, B, all on the circle with radius 1>" is shown on the spreadsheet at "Vector in Hexagon", Excel Vector Trigonometry.

06/12/21
"<4: The maximum inner product with T, O, B, all on the circle with radius 1>"

Vector in Octagon

sqrt(2) - sqrt(8 * (sin(22.5 degrees)^2) * (1 - cos(135 degrees)))
= 0

It shows that the length of the shortest diagonal line of an octagon inscribed in a circle with radius of 1 is square root of 2. How cosine formula and inner product work with vectors in octagon is demonstrated in my spreadsheet.

'Vector in Pentagon' was added to my spreadsheet to calculate magnitude of vector on the diagonal line of a pentagon which is a side of pentagon times phi. (06/11/25)

Phi Figures

(5 / (1 / the golden ratio)) - (5 / the golden ratio) = 5

(10 / (1 / the golden ratio)) - (10 / the golden ratio) = 10

"Phi Figures" - a set of figures calculated with phi
and trigonometric function - is added on this spreadsheet.
- November 21, 2006 -

Phi^10-by-Phi^10 Rectangle and Progressive Difference

(phi^20) - (1 + phi + (phi^3) + (phi^5) + (phi^7) + (phi^9) + (phi^11) + (phi^13) + (phi^15) + (phi^17) + (phi^19)) = 0 *1 *2 shows how I am going to theorize my "Phi-by-Phi (Golden) Rectangle" with Excel Trigonometry.

Excel, Google and websites like Virtual Library of Useful URLs - Fibonacci Numbers and the Pascal Triangle, which will be referred to from time to time, will help beginners like myself further explore the golden ratio and Fibonacci Numbers.

*1 06/11/18
((phi + 1)^10) - (1 + (phi^10) + ((10 * phi) * ((phi^8) + 1)) + ((45 * (phi^2)) * ((phi^6) + 1)) + ((120 * (phi^3)) * ((phi^4) + 1)) + ((210 * (phi^4)) * ((phi^2) + 1)) + (252 * (phi^5))) = 0

*2 06/11/26
the golden ratio^20 = 15 126.9999

(phi^20) - ((1 + phi)^10) = 0

(phi^10) - sqrt((1 + phi)^10) = 0

the golden ratio^10 = 122.991869

the golden ratio^5 = 11.0901699


Excel Calendar

Exploring Phi-by-Phi Squares with Excel Trigonometry

((phi^3)^2) - ((phi^4) + (phi^5)) = 0 is an exmple of how phi^n makes the Fibonacci Sequence - phi^n=phi^n-2+phi^n-1.

Excel is used to show how multiplied phi-by-phi squares are analysed. The phi^2-by-phi^2 square has an area of phi^4.
Phi^4 is equal to: 1 + (4 * (1 / phi)) + (6 * (1 / (phi^2))) + (4 * (1 / (phi^3))) + (1 / (phi^4))). They can be broken down to smaller squares:

phi^3-by-phi^3 "Golden Square", 4*1/phi^2 squares, and 4*1/phi-by-(phi^2-1/2*phi) rectangles

Excel Trigonometry

Exploring Pi with Trigonometry

Trigonometry that seems to have nothing to do with circles or anything having no angles does work in measuring tangent pi on angles on triangles with an area equal to or twice as large as that of a circle and having angles with pi or 2*pi in tangent.

pi-tan(72.343212845degrees) - Google Search -

My Excel sheets show how calculation was made and the relevant trigonometric function.

Excel Trigonometry

Phi-by-Phi Square

I have tried to use my Excel sheet to make calculation on various angles of the golden rectangle, which is 1 by phi. I have found out that by extending the shorter side from 1 to phi, a phi-by-phi square is formed, and the new diagonal line on the extended area (1/phi by phi) is SQRT(3) and forms tangent 2.61803399.. on the corner, as compared with tangent 1.61803399.. on the corner of the original rectangle.

As there seems to be no naming of this, I would like to call this Golden Square.

Excel Trigonometry

Excel as Decoding Tool

"Study this paragraph and all things in it. What is vitally wrong with it? Actually, nothing in it is wrong, but you must admit that it is most unusual. Don't just zip through it quickly, but study it scrupulously. With luck you should spot what is so particular about it and all words found in it. Can you say what it is? Tax your brains and try again. Don't miss a word or a symbol. It isn't all that difficult.... "

I have tried, first glancing and then staring at it, but could'nt find out how there is something particular or unsual about it. Sarah Flannery, a talented young mathematician and author of 'A Mathematical Journey', says in her book that "anyone acquainted with encoding algorithm should have no difficulty finding an answer."

Here is my spreadsheet designed to verify the answer. It is used to locate the position where any of the alphabetical letter, both small and capital, appears first, if any.

I have then used this spreadsheet to find out if there is something similarly particular or unusual about Samuel Ullman's prose "Youth", which has more than twice as many characters and symbols as "study this paragraph ..".

"Youth" by Samuel Ullman

"Youth is not a time of life, it is a state of mind; it is not a matter of rosy cheeks, red lips and supple knees; it is a matter of the will, a quality of the imagination, a vigor of the emotions; it is the freshness of the deep springs of life.

Youth means a temperamental predominance of courage over timidity, of the appetite for adventure over the love of ease. This often exists in a man of sixty more than a boy of twenty. Nobody grows old merely by a number of years. We grow old by deserting our ideals.

Years may wrinkle the skin, but to give up enthusiasm wrinkles the soul. Worry, fear, self-distrust bows the heart and turns the spirit back to dust.

Whether sixty or sixteen, there is in every human being's heart the lure of wonder, the unfailing child-like appetite of what's next, and the joy of the game of living. In the center of your heart and my heart there is a wireless station; so long as it receives messages of beauty, hope, cheer, courage and power from men and from the infinite, so long are you young.

When the aerials are down, and your spirit is covered with the snows of cynicism and the ice of pessimism, then you are grown old, even at twenty, but as long as your aerials are up, to catch the waves of optimism, there is hope you may die young at eighty."

The result shows that the paragraphs do not contain a z, but they do contain all of the other letters.


Samuel Ullman and "Youth": The Life, the legacy

In Code: A Mathematical Journey


Prose in Pi

Google Spreadsheets

What's New

My Website Excel and Google Spreadsheets
- August 21, 2007 -


DailyTech - Google Distributes Sun's StarOffice for Free
DailyTech August 16, 2007 2:21 PM


Star Office 8 Sun Micro Systems


I will try it here in Japan. What difference does it make from Google Spreadsheets?
I will find out.

August 19, 2007



Beijing Olympics Schedule - Google Docs & Spreadsheets


Calendar Template on Google Spreadsheets

August 16, 2007



Here comes, finally or at last for Excel fans who love Google as well, Google Spreadsheets.

Google Spreadsheets - Sneak Peek

To sign in Welcome to Google Spreadsheets

Google Directory - Computers > Software > Spreadsheets > Excel > Add-Ins

Excel Cell Locator

The expanse of Excel, as "spreadsheet" implies, is fully used to store and locate data.

Each cell on its sheet is addressed by the column and row, so it is easy to locate the cell with its address (e.g. A1).

The number of columns on a single sheet is 256 and rows, 65,536.

Excel cell locator - Google Search lists websites giving ideas on how to understand and use "Excell, whoops, Excel cell locator".

Excel Cell Locator

Excel Combined with Google Calculator: Trigonometry

I have estimated one of the two angles of a diagonal line on a golden rectangle to be approximately 31.71747441 degrees.

My Excel sheet is used to make calculation and shows that the figure amounts to a reciprocal of phi.

The other angle is also shown in Excel to correspond to phi in tangent. Here comes into play Google Calculator again.
- October 7, 2006 -

Excel can be used just not for calendars or planners. It also comes into play when used as math tools. It would prove more useful when combined with google calculator.

Here is Excel Trigonometry.
- August 17, 2006 -

Google as our Homepage

"Live scores and match schedule
right on your Google homepage."

Google offers World Cup 2006 as our homepage to update as the games go on.

To search more, 2006 FIFA World cup schedule score - Google Search

Google Calendar

One more Google to add to the joy of the Internet to help expand my arena and still focus on important topics and subjects.

It is Google Calendar.

I was lucky to spot Interesting Google Calendars and found out that this helps add the 'FIFA World Cup 2006' and 'iWorldEvents Calendar' to the Google Calendar.

I was searching Google for "Fifa world cup charts and schedule excel" when I spotted "World Cup Games on your Calendar and Predictor Charts-FIFA World...", on top of my my Excel 2006 FIFA World Cup Germany Timeline....

Google Calendar, of course, in itself will be a nice, useful planner to help me work out and organize my schedule. And how will it be turning out to be different from my Excel calendars.

Excel World Cup Countdown & Chart

World Cup Schedule and Chart in Excel

Google & Excel 06/05/02

Google:

Google Search: More, more, more
Alerts
Answers
Blog Search
Book Search
Catalogs
Directory
Froogle
Groups
Images
Help Center: Web Search Features > Calculator
Labs
Local
Maps
Mobile
News
Scholar
SMS
Special Searches
University Search

Google Tools:
Blogger
Code
Desktop
Earth
Gmail
Local for mobile
Pack
Picasa
Talk
Toolbar
Translate

Excel Calendar & Stock Chart