Nate B

World Math Day Geogebra Contest Entry

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

Geogebra construction late

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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

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Nate Bulman, Created with GeoGebra


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

Reflection Coordinate Applet

Sorry for the lateness

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Nate Bulman, December, 2010, Created with GeoGebra


Sequence Construction

BAM

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Nate Bulman, Created with GeoGebra


Triangle Centers Construction

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Parametric intersection problem

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Nate Bulman, Created with GeoGebra

Nate B. Portfolio Problem



Problem Nine on page two: geogebra_hm2_q_9.png
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}
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



pentagon, pentagram, decagon and dodecahedron. It is denoted
phi
phi
, or sometimes
tau
tau
.
The designations "phi" (for the golden ratio conjugate
1/phi
1/phi
) and "Phi" (for the larger quantity
phi
phi
) 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
("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
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.
phi
phi
has surprising connections with continued fractions and the Euclidean algorithm for computing the greatest common divisor of two integers.
GoldenRatio
GoldenRatio


Given a rectangle having sides in the ratio
1:x
1:x
,
phi
phi
is defined as the unique number
x
x
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
1:x
1:x
(i.e., such that the yellow rectangles shown above are similar). Such a rectangle is called a golden rectangle, and successive points dividing a golden rectangle into squares lie on a logarithmic spiral, giving a figure known as a whirling square.
Go to wolfram's page to see the full explination of the golden ratio.
http://mathworld.wolfram.com/GoldenRatio.html