Freelancer.com: Expose our logo competition 2009/2010

[download PDF-for-web version] [as *.swf format][go to submission No. 2]

Contest introduction

Here's your chance to promote the new logo for the world's number one freelancing website and win US$10,000! Expose our logo to as many people as possible, as creatively as possible! Create a real life media stunt or find some other way to get publicity! To enter, all you need to do is to send us a photo, image or video of your work, or a link to it in the news.

Word Expose^{[By Merriam Webster Dictionary]}:

Main Entry: ex·pose

Pronunciation: \ik-spōz\

Inflected Form(s): ex·posed; ex·pos·ing

1 a : to deprive of shelter, protection, or care : subject to risk from a harmful action or condition <expose troops needlessly> <has not yet been exposed to measles> b : to submit or make accessible to a particular action or influence <expose children to good books>; especially : to subject (a sensitive photographic film, plate, or paper) to radiant energy c : to abandon (an infant) especially by leaving in the open

2 a: to make known: bring to light (as something shameful) b : to disclose the faults or crimes of <expose a murderer>

3: to cause to be visible or open to view: display: as a: to offer publicly for sale b: to exhibit for public veneration c : to reveal the face of (a playing card) or the cards of (a player's hand) d : to engage in indecent exposure of (oneself)

Exploring Freelencer.com logo:
Pristovnik Andrej's Aim to EXPOSE irregularity in LOGO from the mathematical point of view or
How can we change LOGO just a “little bit” ;-)

Introduction

My native language is Slovenian, however I believe (NO, I know that ;-) that I can have (get) more publicity if I publish that article in English. I think that my English is not as good as I’d like so please forgive me for any errors. I have tried to do by my best effort. Please let me know if you find any spelling or grammar errors (test@raziskave.org, www.raziskave.org ).

Close look of the Freelancer's logo show us, that only designers point of view was considered. Logo (Fig. 1) is composed from simple mathematical shapes, one pentagon and five triangles (Fig. 2).

We can always devide that pentagon into three triangles (Fig. 3), so in basic, the logo is composed from eight triangles.

That's realy O.K., but vertex angles are not integers or they are not rounding to integer …

If we close examed those triangles, measure them (or entering three points that make the vertex of a triangle) we can see, that design is not finished yet ;-) It requires minor corrections.

Procedure I.

• Side length data taken from original Freelancer's LOGO with CorelDraw tool “Dimension”

Figure 4: Eight triangles from Freelancer's LOGO

• Calculations^[a]

Table No. 1: Side length data and calculated vertex angles from original Freelancer's LOGO

Table No. 2: Proposed new vertex angels of the triangles with new calculated side lenght

• Drawing a new triangles using Mathematica Player and “Drawing a Triangle” from The Wolfram Demonstrations Project web page^[4] (Figure 6).

Figure 6: “Drawing a Triangle” tool^[4]

• Import drawings into Corel Draw and “set-up” a little bit modified LOGO
  (Figures 7 a, b, c, d, e, f, g and h)

Weld triangles 6, 7 and 8 and fulfill all shapes with adequate colors

Procedure II. or back/check-up procedure

• Data taken from original Freelancer's LOGO (Table No. 3) with determining (and reading ;-) all of the 24 vertices (Figures 9 a-f).

Figure 9: Original Freelancer's LOGO and Freelancer's LOGO drawn from the koordinates of the vertices

Table No. 3:Points (vertices) of the triangles as a a pair of numerical coordinates
(page format A4 xÎ[0, 297] & yÎ[0, 210])

• Calculations^{[b, a]}

Table No. 4:Calculated side length from coordinates (left) and difference with the measured one (right)
(see Table No. 1)

Table No. 5:Calculated vertex angles from original Freelancer's LOGO (Left) and
2^nd proposition of the vertex angels of the triangles (Right)

Every body can try to plot changed Freelancer's LOGO with the Wolfram Demonstration Project web page
(http://demonstrations.wolfram.com/DrawingATriangle/ ) and with the data from the yellow cells in Table No. 5!

Solution

Figure 8: Old vs New Freelancer's LOGO (from the No. 1 procedure)

I didn't want to use only (in the first place) the integer numbers for the angles value of the triangles no. 5, 6 and 7. Somebody else can do that (and use data from the Table No.5).

From this point of view we now have:

• Three right trinagles: 3, 4 and 8 (last one is isosceles right triangle too),
• Two isosceles triangles: 7 and 8 (last one is isosceles right triangle too),
• Two obuse scalene triangles: 1 and 5,
• Three acute scalene triangles: 2, 6 and 7 (last one is isosceles triangle too).

And one little sugestion

Now, (in CMYK color space and for the printing purposes) 4 different colors are used.
My proposition is that:

• pentagon uses same color as it is now (C:50,M:10,Y:0,K:0) ,
• two right trinagles: 3 and 4 have identical color,
• two obuse scalene triangles: 1 and 5, have identical color and
• one acute scalene triangle: 2 use color, which distinguish from other colors.

That's all folks! Try it! Develop further that …!

[download PDF-for-web version]

Theory

[a]       Triangle, the law of cosines and the law of sines

Figure 5: A triangle with sides of length a, b and c and angles of α, β and γ respectively.

The law of cosines[2], or cosine rule, connects the length of an unknown side of a triangle to the length of the other sides and the angle opposite to the unknown side. As per the law:

For a triangle with length of sides a, b, c and angles of α, β, γ respectively, given two known lengths of a triangle a and b, and the angle between the two known sides γ (or the angle opposite to the unknown side c), to calculate the third side c, the following formula can be used:

The law of sines[2], or sine rule, states that the ratio of the length of a side to the sine of its corresponding opposite angle is constant, that is

This ratio is equal to the diameter of the circumscribed circle of the given triangle. Another interpretation of this theorem is that every triangle with angles α, β and γ is similar to a triangle with side lengths equal to sinα, sinβ and sinγ.

The sum of angles in a triangle is 180 degree.

[b]       Cartesian coordinates, the Euclidean distance[6]

A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin. The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as a signed distances from the origin.

The Euclidean distance between two points of the plane with Cartesian coordinates (x1,y1) and (x2,y2) is:

Bibliography

[1]   http://www.raziskave.org/

[2]   http://en.wikipedia.org/wiki/Triangle

[3]   http://mathworld.wolfram.com/Triangle.html

[4]   "Drawing a Triangle" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/DrawingATriangle/

[5]   http://www.mathleague.com/help/geometry/angles.htm

[6]   http://en.wikipedia.org/wiki/Cartesian_coordinate_system