I ’ve been fascinated with this premise for years now , and this calendar week I saw this pop graphical pop up yet again :
I ’d seen this graphicdebunked , but it was n’t particularly rigorous , so I decided it was finally clip to sit down and answer this for myself definitively .
In researching this , the first thing to go look for seemed to be whether or not the designer of the logo , Rob Janoff , has spoken about his cognitive process . Indeed , Janoffhas addressed in an interviewthe evolution of the shape :
The Malus pumila shape changed slightly from my original design in the early 80 ’s . The intent house Landor & Associates made the alteration . They brightened the colour , they made the form much more symmetric , much more geometric . When I design it I fairly much did it freehand .
Pulling up examples from honest-to-god Apple paraphernalia confirm that his logotype was obviously not reliant on rigorous geometry :
Okay , the original logo was not the numerical masterpiece ( mathterpiece ? ) that we know today , but possibly Landor & Associates introduced the golden ratio when they touch on it up . I could n’t find any information online about their design cognitive process , but in take care at examples of the Apple logotype after L&A mold on it in the other ’ LXXX , you’re able to see it was much closer to the logo we hump today :
This is from the sales manual for the original Macintosh . Here the shape is more substantial and symmetrical , the lines are not freehand , defined by simple-minded , stricter curves .
But does it stand by to the gold ratio ? scatty firsthand information from the intriguer , our estimable bet is to just canvas the logo ourselves . Every Apple computer contains a vector cut of the logo , in the form of a Unicode symbolization — .
to boot , Apple provides public press materials directly on their web site , including assets that contain a transmitter edition of the logo . Some of the files contain in the mechanical press outfit are for retina display , so I guess it ’s good to assume that the logotype asset used is contemporary enough for our discussion .
Curiously , the Unicode symbolization and the press kit symbolization in reality cleave to different geometries :
This level of unevenness suggests that the logotype ’s geometry is n’t exceptionally rigid , which sucks some of the magic out of the feeling that Apple has ruthlessly machine this double-dyed shape . But allow ’s plant that aside and apply the most late cut of the logotype , assuming that one is the most elegant .
The unproblematic home to begin anchoring our measuring rod is the dress circle marked “ 13 ” in the diagram , as the diameter runs from one point in the shape to another which makes it simple to create a circle of that precise size .
The next step is to set forth matching circles to curves , and seeing if their relative diam match with the diagram .
As it sprain out , most of the big curves in the Apple logo are not actually circular arcs . occupy the folio as an representative , you may see the arc intersects with the roofy at both beginning and end but otherwise does not systematically follow the same curve :
This arc of the leaf is really two separate arc with dissimilar radius , you could see a midpoint there . This is really the pillow slip with most of the curve in the logo . If the breaking ball are not rotary arc , then one ca n’t really utilise circles to return this logo , nor can one accurately valuate their equivalency .
But let ’s forgive that , and approximate as good we can , accepting more variation . I started with the 8s , sizing circle until they ran roughly parallel with the logotype . Here were my results :
Already we have major problem . The difference of opinion between 7.5 and 8.5 is the difference been having a golden proportion economic value of 1.53 and 1.73 . To visualize what a meaning difference of opinion that is , here ’s a “ golden ” rectangle formed out of 1.73 :
And another take shape from 1.53 :
This is a striking amount of variability if we really are meant to rate organized religion in an irrational routine . But let ’s forgive this , too , and bet at the very rasping divisions of space confront by the graphic . That bottom pass on recess where the 8 and the 5 meet the 3 — the only 3 mind you — is deeply shady . Let ’s take a closer looking at . Start by tot up the 5 …
Err , I mean , the 4.4 …
And now the 3 …
So , once you factor out in the tangible , non - circular curved shape of the plan , the variableness really starts to demonstrate that the family relationship are completely nonmeaningful . Irrational numbers pool are not fuzzy affair that can be slackly judge at this order of magnitude . 3:4.4:7.5 is no longer maths .
But heck , let ’s even forgive this and restore their circles to the fuzzy idea :
These do n’t even touch when I accept the original value , but whatever .
Here ’s my point : why 3 ? Why not this ?
The condition for a outer space haviIt ’s not as though the “ 1 ” size in the diagram is derived from some key understructure unit : it ’s just a random interruption between randomly defined circles .
So when you forgive the gilded ratio not being used in the design process , and you forgive the fact that the logotype can not actually be derived from circles , and you forgive the fact that even approximated circuit do n’t line up with the proposed note value , and you forgive the fact that any shape can be filled with circles of arbitrarily lowly diameters … what are you leave with ?
Let ’s take a moment to deal the working capital T in Helvetica : initely decreasing size of it . Behold , the folio itself is a deriving from the gold ratio :
This missive is constructed to look as though the horizontal and perpendicular strokes have the same width . Here ’s how they really compare :
They ’re actually rather different . But the letter put to work , because the eye does not actually perceive exact geometry to be precise geometry . If they were the same width , the horizontal stroke would in reality appear to be thicker and it would look bizarre . That ’s the converse : real visual rhythm method is hurt by preciseness . This fact is where we get the locution in blueprint : if it looks right , it isright .
So in a funny way , the Apple logotype feels like it cling to some system because it does n’t .
I ’ll close with this , a mockup I made the last clock time I got real huffy about the favourable ratio ’s service program in making conclusion :
This berth was in the beginning published onQuora .
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