Hoeveel ruimte zouden alle iPhone’s innemen?

Dat de iPhone door de jaren heen de best verkochte smarthpone is, daar bestaat geen twijfel over. Er zijn gelukkig altijd een aantal nietsnutten die dit op één of andere manier proberen te visualiseren.

Uitvoerder is Josh Orter van Stupid Calculations, een serie waarin praktische statistieken worden omgezet in nutteloze feitjes. Hij berekende hoe groot een scherm zou zijn, gemaakt van displays uit alle iPhone’s die ooit zijn verkocht. Voor de wiskundeleken onder ons – beta’s kunnen zich hieronder uitleven met de berekening – alvast het antwoord: 1542 x 868 meter. Even voor de vergelijking: Central Park in NY is 805 meter breed. Indrukwekkend!

De website meldt dat we berekeningen kunnen verwachten over onderwerpen als sinaasappelschillen, walvissen, escorts, liften, zwembaden en tranen van vreugde.

Let’s start with the number of iPhones out in the world. Apple’s financials show that 352,292,000 have sold since day one through the most recent quarter. Sparing a potentially huge pain in the ass, every pre-iPhone 5 model conveniently has the same display size. So we automatically know that everything sold before iPhone 5 launched on 9/21/2012 had a 3.5” diagonal screen. That’s 271,073,000 units.There’ve been another 85,219,000 sold since then with a roughly 60/40 split in favor of the 5.

85,219,000 x .60 = 51,131,400 iPhone 5
85,219,000 x .40 = 34,087,600 all other models
So we add 34,087,600 the 271,073,000 for a total of 305,160,600 older models.
And we’ve got the 51,131,400 iPhone 5’s.

Next up, we need to figure out the average size of an iPhone screen. Every iPhone model built before the 5 has had a 3.5” diagonal screen with an 3:2 aspect ratio. That makes it 2.94” x 1.94” for a screen area of 5.65 square inches. iPhone 5 has a 4” diagonal and a 16:9 aspect ratio (same as an HDTV).
That makes it 3.49” x 1.96” for 6.83 square inches area.

305,160,600 older models x 5.65 square inches=1,724,157,390² inches
51,131,400 iPhone 5’s x 6.83 square inches= 349,227,462² inches
TOTAL 2,073,384,852 square inches (14,398,506 sq ft or 330.54 acres or 0.516 square miles)

Super, we’ve got the area. Dimensions are another story and having slipped out of high school algebra only through a teacher’s pity, this took a shameful amount of time to figure. Phone calls had to be made.

What are the dimensions of rectangle with an area of 14.98 million sq ft given a ratio of 16:9?
16x * 9x = 14,398,506 sq ft
x^2 = 99,989.62 (this is the total square footage divided by 144, the product of 16 x 9)
x = 316.211 (the square root of the number above)
16x = 5,059 feet (the product of 16 x 331.271)
9x = 2,846 feet (the product of 9 x 331.271)

Central Park’s almost exactly half a mile across, making the screen just a touch wider. So lay the base of a 16:9 rectangle at the south end of Central Park South and proportionally scale it 7.23% wider than the park’s borders. Then double-check by using the 705-foot height of the General Motors building at the southeast corner of the park: monophone needs to be 7.15 times taller. By happy coincidence, Apple’s 5th Avenue glass cube store is bunkered under the GM Building’s plaza.