Snapchat, Dragon flies, plants and CONSPIRACIES

I was reading my book, and it made a reference to a math rule called the "golden ratio". The author made it seem glorious stating, "Our mathematics is the symbolic counterpart of the universe we perceive, and its power has been continuously enhanced by human exploration." (Bello 8.9). I had no idea why Bello made it seem so mysterious, so i did research on it.

The golden ratio is a math rule, or more like shape. it is directly correlated to the Fibonacci series. The Fibonacci series, like i talked about in my last post,  is a series of numbers where the next number is equal to the sum of the two previous numbers. the order is 1,1,2,3,5,8,13,21,34.... the fascinating thing is if you take a number in the series, and divide it by the previous number, you get a decimal surprisingly close to a term called "phi".the official ratio is 1:1.61803398875 (meaning for every one unit, the next unit is exactly 1.6180339887 (aka phi) times that number

this shows up EVERYWHERE. after staying up all night wondering how i had not been taught this already i found that it is possible to be mathematically beautiful.  Dr. Stephen Marquardt used the golden ratio shapes and made a mask. the mask is named the Beauty mask. if you take a model, someone who is widely seen as attractive, and you put the beauty mask on top of it, the facial features will match almost exactly. the more your face matches the map, the more people tend to find you attractive (statistically). Ever wonder how Snapchat is able to make you look "beautiful" in filters? or how it (usually) knows where all of your facial features are? well that white grid that covers your face is a version of the facial map. 

A little information on how the facial map works on your face:

 Your mouth is exactly phi times the width of the base of your nose. if you measure the width of your mouth and multiply it by phi that is equal to the distance between the corner of your mouth and your jaw line. your two front teeth are phi times wider than the two next to them. There's much more but includes a lot of variables and can get hard to understand, so here's a photo

The golden ratio also correlated to Plants, the way leaves grow and how pine cones are formed follow a perfect spiral.  Advertisers use this equation to make billboards seem more visually pleasing or adjust the way people hold things. if you look at a dragon fly under a microscope you will notice that the wings AND eyes have the same similar pattern. make a fist right now. now look at it with the knuckle of your thumb facing you. see that little spiral your hand makes? you guessed it, that is exactly what the Fibonacci spiral looks like.

Now to tie this incredible knowledge back to my topic, Drawing. I have a theory: anybody can improve their drawings if they first take the time to understand the mathematics of how it works. Knowing how something works is what really makes it beautiful. To test my theory i decided to draw the golden ratio facial map. I drew one face completely free hand and the other using most of the mathematics.
Before you look at the photos i would like to put an emphasis on the fact that i am by no means an artist. The closest  thing i have to drawing knowledge is the shading post that Josie wrote. 

I think it is safe to say that if i ever am tasked with drawing a face, i will have a calculator and a ruler handy.

Have you ever heard of the golden ratio? if not why don't you think our math classes have not taught us this yet?

materials used

• pencil
• ruler
• protractor
• compass
• paper

Bello, Engr R. Technical Drawing: Presentation & Practice. 1st ed. N.p.: CreateSpace, 2012. Web.

Meisner, Gary B. "Facial Analysis and the Beauty Mask." Goldennumber.net. Phi-point Solutions, 12 Jan. 2012. Web. 03 Dec. 2016.

Technical Drawing

Ever since i can remember i have drawn within the lines. a single line out of place and i would not be able to complete the drawing because it would bug me to the point of near insanity. I've realized that i was more fascinated by the lines themselves than the picture, thus began my love of geometry. I've always been especially good with numbers, specifically the fact that there is no guessing - there IS a right answer.

For this blog i am reading a book titled Technical Drawing: Presentation & Practice by Engr Segun R. Bello. This book is not quite a beginners level understanding of it, so while i will have the different methods i used to draw certain figures, i'll leave out the 'boring' equations.

I am going to mainly be focusing on improving my visualization of every day things, seeing how they work, why they look the way they do, and how i can draw it. You'd be amazed how much parabolas show up in nature.

This blog seems to be a lot of information, and little entertainment thus far... so let's begin 

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Fibonacci series

the Fibonacci series is a series of numbers where each number equals the sum of the previous two numbers. example: 1, 1, 2, 3, 5, 8, 13. when graphed it takes a spiral or a "whirl" shape to it, which is most famously seen in pine cones

to draw this, i used a series of boxes gradually getting smaller as they descend down the curve created by a series of hexagons and squares tilted by approximately 20° 

in the book, it states," Principal lines are sketched lightly using a number of short strokes. once the joining points have been established and lines are satisfactorily straight, they may be darkened as needed to give complete emphasis"(Bello 7.5). I am not used to doing a practice run before the finished design, so tracing over the lines i want will be new to me.

This is the finished principal lined drawing. you can see all of the boxes and angles, as well as the 20.6cm circle it was drawn within. 

This part is much harder in my opinion. It takes a lot of standing back and looking at it to remember exactly which lines need traced, and when using a permanent marker a single messed up line could potentially ruin the beauty of the pattern.

Thankfully i'm not reading a book on coloring the photos. I was planning on coloring it in a rainbow pattern on the curves to show it better, but as i finished i noticed this 3-point clover like shape, which i have found in other drawings. this show's that there are correlations between so many random things in the world that anyone can see, you just have to be looking. 

these other two drawing where not made similarly at all, yet have the same inner shape 

I think the biggest strength i had was with making the larger shapes. Once it got down the smaller lines however, it became increasingly difficult to line things up. with the inner two rows of boxes you can see that they are not quite consistent enough in the shape of them, and the occasional line does not actually match up in the location it should. I will probably use a finer tipped maker/sharpie in the future so i could possibly add more detail as needed. I think that i was rushing too much as well, i got sloppy which is not a good thing to do when dealing with math. i will give myself more time to do the projects in the future.

has seeing these shapes be combined to make art changed your opinion on geometry or math in general?

Materials used:

• Compass
• ruler
• sketching pencil
• black marker
• a piece of paper

NOTICE: no actual pine cones where harmed in the making of this drawing 🎄

Bello, Engr R. Technical Drawing: Presentation & Practice. 1st ed. N.p.: CreateSpace, 2012. Web.