Wallwisher Problem
my late screencast for quadrilateral proofs
this wouldve been up earlier this evening/night, but i forgot to upload the video and applet until i was trying to fall asleep. oops

Problem Nine on page two:
I made the point from which I was going to measure the segments first. Then I made the line to put the new points on. I put one point on the line, connected it to the first point, added the distance tool, and dragged it until the distance became ten. For the other point I simply counted how many over and up I had gone for the first point and did the same in the other direction.

Sitmo and dynamic sketch for problem 5 on page three. it is about an equidistant point from a and b. I made the two points, a=(1,5) and b=(3,-1). I then formed their perpendicular bisector, any point on that line is equidistant from a and b.

my sitmo equation is as follows:

eq=y=frac{4}{3}+frac{x}{3}

that is the simple equation for the line that is equidistant from point a and b

The Golden Ratio
The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the

) are sometimes also used (Knott), although this usage is not necessarily recommended.
The term "golden section" (in German, goldener Schnitt or der goldene Schnitt) seems to first have been used by Martin Ohm in the 1835 2nd edition of his textbook Die Reine Elementar-Mathematik (Livio 2002, p. 6). The first known use of this term in English is in James Sulley's 1875 article on aesthetics in the 9th edition of the Encyclopedia Britannica. The symbol

phi

("phi") was apparently first used by Mark Barr at the beginning of the 20th century in commemoration of the Greek sculptor Phidias (ca. 490-430 BC), who a number of art historians claim made extensive use of the golden ratio in his works (Livio 2002, pp. 5-6). Similarly, the alternate notation

tau

is an abbreviation of the Greek tome, meaning "to cut."
In the Season 1 episode "Sabotage" (2005) of the television crime drama NUMB3RS, math genius Charlie Eppes mentions that the golden ratio is found in the pyramids of Giza and the Parthenon at Athens. Similarly, the character Robert Langdon in the novel The Da Vinci Code makes similar such statements (Brown 2003, pp. 93-95). However, claims of the significance of the golden ratio appearing prominently in art, architecture, sculpture, anatomy, etc., tend to be greatly exaggerated.

such that partitioning the original rectangle into a square and new rectangle as illustrated above results in a new rectangle which also has sides in the ratio

## Nate B

## World Math Day Geogebra Contest Entry

## Table of Contents

my late screencast for quadrilateral proofs

this wouldve been up earlier this evening/night, but i forgot to upload the video and applet until i was trying to fall asleep. oops

## Geogebra construction late

Nate Bulman, Created with GeoGebra

And at long last, I now have posted some GEOMETRY PICTURES from my recent trip to Tanzania!

or at least they will be up sooner or later

## Africa Pictures!

## Winter Break Problem

## Xmas break applet

Nate Bulman, Created with GeoGebra

Sorry that my voice sounds so... wierd...

## Reflection Coordinate Applet

Sorry for the lateness

Nate Bulman, December, 2010, Created with GeoGebra

## Sequence Construction

BAM

Nate Bulman, Created with GeoGebra

## Triangle Centers Construction

Nate Bulman, Created with GeoGebra

## Parametric intersection problem

Nate Bulman, Created with GeoGebra

## Nate B. Portfolio Problem

Problem Nine on page two:

I made the point from which I was going to measure the segments first. Then I made the line to put the new points on. I put one point on the line, connected it to the first point, added the distance tool, and dragged it until the distance became ten. For the other point I simply counted how many over and up I had gone for the first point and did the same in the other direction.

Sitmo and dynamic sketch for problem 5 on page three. it is about an equidistant point from a and b. I made the two points, a=(1,5) and b=(3,-1). I then formed their perpendicular bisector, any point on that line is equidistant from a and b.

my sitmo equation is as follows:

that is the simple equation for the line that is equidistant from point a and b

The Golden RatioThe golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the

pentagon, pentagram, decagon and dodecahedron. It is denoted

The designations "phi" (for the golden ratio conjugate

The term "golden section" (in German,

goldener Schnittorder goldene Schnitt) seems to first have been used by Martin Ohm in the 1835 2nd edition of his textbookDie Reine Elementar-Mathematik(Livio 2002, p. 6). The first known use of this term in English is in James Sulley's 1875 article on aesthetics in the 9th edition of theEncyclopedia Britannica.The symboltome, meaning "to cut."In the Season 1 episode "Sabotage" (2005) of the television crime drama

NUMB3RS, math genius Charlie Eppes mentions that the golden ratio is found in the pyramids of Giza and the Parthenon at Athens. Similarly, the character Robert Langdon in the novelThe Da Vinci Codemakes similar such statements (Brown 2003, pp. 93-95). However, claims of the significance of the golden ratio appearing prominently in art, architecture, sculpture, anatomy, etc., tend to be greatly exaggerated.Given a rectangle having sides in the ratio

Go to wolfram's page to see the full explination of the golden ratio.

http://mathworld.wolfram.com/GoldenRatio.html