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we called "square dots". Square dots made it easier to write graphical applications, since you didn't have to worry about the resolution disparity.
    Bill Atkinson, the author of Quickdraw and the main Lisa graphics programmer, was a strong advocate of square dots, but not everyone on the Lisa team felt the same way. Tom Malloy, who was Apple's first hire from Xerox PARC and the principal author of the Lisa word processor, thought that it was better to have the increased horizontal resolution. But Burrell's redesign moved the debate from the theoretical to the pragmatic, by creating a square dots machine to compare with the Lisa.
    The Lisa hardware was scheduled to go through a final round of design tweaks, and Bill tried to convince them to switch to square dots. He mentioned his desire to Burrell, who responded by working over the weekend to sketch out a scaled up version of the Macintosh design that featured a full 16-bit memory bus with a 768 by 512 display and square dots, that would also run twice as fast as the current Lisa design. Bill convinced the Lisa engineering manager, Wayne Rosing, that he should at least consider adopting some of Burrell's ideas, and arranged for the leadership of the Lisa team to get a demo of the current Macintosh, and learn about Burrell's new scaled-up design.
    Wayne Rosing led a delegation of his top hardware and software guys over to Texaco Towers for a demo on a Monday afternoon, including hardware guys Rich Page and Paul Baker and software manager Bruce Daniels. We ran various graphics demos, with Bill Atkinson doing the talking, and then Burrell gave a presentation on the Mac design, and his ideas for scaling it up to 768 by 512 display. Everyone seemed pretty impressed and Bill was optimistic that they would make the change.
    After a few days, Bill told us the disappointing news that Wayne had decided that there wasn't enough time to embark on such a radical redesign, since at that point the Lisa was scheduled to ship in less than a year. It ended up shipping around two years later with the original 720 by 360 resolution and relatively slow microprocessor, which became a problem when Apple decided to offer a Macintosh compatibility mode for Lisa in 1984. The emulation software didn't try to compensate for the different resolutions, so the applications were distorted by the resolution disparity, almost like looking at a fun-house mirror. It would have continued to be a problem for Apple if the Lisa hadn't been discontinued in 1985.

Round Rects Are Everywhere!
by Andy Hertzfeld in May 1981

    Bill Atkinson worked mostly at home, but whenever he made significant progress he rushed in to Apple to show it off to anyone who would appreciate it. This time, he visited the Macintosh offices at Texaco Towers to show off his brand new oval routines, which were implemented using a really clever algorithm.
    Bill had added new code to QuickDraw (which was still called LisaGraf at this point) to draw circles and ovals very quickly. That was a bit hard to do on the Macintosh, since the math for circles usually involved taking square roots, and the 68000 processor in the Lisa and Macintosh didn't support floating point operations. But Bill had come up with a clever way to do the circle calculation that only used addition and subtraction, not even multiplication or division, which the 68000 could do, but was kind of slow at.
    Bill's technique used the fact the sum of a sequence of odd numbers is always the next perfect square (For example, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7 = 16, etc). So he could figure out when to bump the dependent coordinate value by iterating in a loop until a threshold was exceeded. This allowed QuickDraw to draw ovals very quickly.
    Bill fired up his demo and it quickly filled the Lisa screen with randomly-sized ovals, faster than you thought was possible. But something was bothering Steve Jobs. "Well, circles and ovals are good, but how about drawing rectangles with rounded