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Retina Display

by Robert Kaplinsky

Retina Display

Act One

  • 1.

    What is pixel density and why does it matter?

  • 2.

    How is pixel density measured?

Act Two

  • Teacher note
    A little background on pixels and pixel density might be helpul:

    pixels: the display on a device such as a smartphone, tablet, computer monitor, or LCD TV has hundreds of thousands of little points of colors called pixels. The more pixels a display has, the sharper the resolution of the image being displayed.

    pixel density: engineers measure a display’s resolution using the unit “pixels per inch” or ppi (in metric it is pixels per centimeter). Initially I had the misconception that this was the number of pixels in one square inch of display. That is incorrect. Instead, the unit ppi stands for the number of pixels per linear inch (usually along the diagonal). You can find it by dividing the number of pixels along the diagonal by the diagonal’s length in inches.

    Apple’s Retina Display claims that its pixels are so small and close together that “your eye can’t distinguish individual pixels.” The picture below helps demonstrate why increased pixel density is a good thing. You can see that the text is much sharper on the phone with the Retina Display (note that this is actually a comparison of the iPhone 3 to the iPhone 4 which also had a Retina Display).
  • ImageNo Retina Display compared to Retina Display
  • Teacher note
    To determine the iPhone 5′s pixel density, we need two pieces of information about the display:

    The diagonal’s length measured in pixels

    The diagonal’s length measured in inches

    With those two pieces of information we can divide the pixel measurement by the inch measurement and get the pixel density. So, the goal at this point is for students to realize that they need to find this information.

    The image below from Apple‘s website has that information and shows that the phone has a “4-inch display” and an “1136-by-640 resolution”. I have included two versions of this image depending on the amount of challenge you would like to provide your students in terms of being able to “cite the textual evidence that most strongly supports an analysis of what the text says explicitly” (CCSS ELA Literacy RI.8.1):
  • ImageOne with full text as it is displayed on Apple’s website
  • ImageOne with much of the text removed to make it more manageable (thanks to Andrew Stadel for that suggestion).
  • Teacher note
    At this point, we have “the diagonal’s length measured in inches” as well as the number of pixels along both sides of the display (1136 and 640) but we still need to find “the diagonal’s length measured in pixels.” This is where students will need to use the Pythagorean Theorem. The phone display’s sides create a triangle that is 1136 pixels long on one leg, 640 pixels long on the other leg, and an unknown diagonal.
  • ImageiPhone 5 with superimposed triangle
  • Teacher note
    Using the Pythagorean Theorem, you get c^2 = 1136^2 + 640^2 where c ≈ 1304 pixels long. We now have all the information we need to find the iPhone 5′s pixel density:

    326 ppi ≈ ~1304 pixels / 4 inches
  • ImageWikipedia provides confirmation of our approach to this problem

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