Square Face with Round Time is an analogue clock with a completely square face. Here's how it works:
Taking advantage of an idea I posted a while back (link) Square Face clock features telescopic hands.

This time, the ability for the hands to elongate and contract in length has been motorised and linked to their circular motion. This means that they constantly adjust in length as they rotate, resulting in them always pointing precisely to the numbers enscribed along the perimeter of the square. By doing so they simultaneously describe a circle and a square.

De-luxe variations feature oblongs and other odd shapes yet with the hands always pointing out to the edges of the face perimeter.
-- xenzag, May 08 2021

Expanding_20Clock [xenzag, May 08 2021]

3Blue1Brown: Using a Fourier series to trace out an image of Fourier https://www.youtube...art_radio=1&t=1315s
Using circular motion to describe non-circular pathways. [zen_tom, May 09 2021]

Go Figure https://gofigure.impara.ai/drawing/30664
Generate your own Fourier-series renderings of simple line drawings. [zen_tom, May 09 2021]

[ ] travels on undulating surface nnn as a square wheel https://en.wikipedi...g/wiki/Square_wheel
[beanangel, May 09 2021]

Haar wavelet transform does square waves without fourier https://dsp.stackex...l-into-square-waves
[beanangel, May 09 2021]

Options! https://www.google....eDpYQ4dUDCAc&uact=5
Ways to make extending/retracting hands. [neutrinos_shadow, May 10 2021]

The hour hand still describes a square but is constantly shorter, as it is with a circular clock.
-- xenzag, May 08 2021


Surprised you didn't incorporate a complex square- motion mechanism.
-- RayfordSteele, May 08 2021


One contradiction is interesting, but two combined movements may cancel out the effect. It's all interesting, ie the idea of drawing a square on a continually rotating piece of paper.
-- xenzag, May 09 2021


I feel like extending the hands using individual motors is inelegant. If you used a guide track leading a pin attached to the telescoping segment of each arm, I think you could get a fairly good approximation of a square, driven by the clock mechanism.
You'd probably need to round the corners at least a bit, but the overall error would be good, and the motion would be superior.
-- Loris, May 09 2021


//Or you could cheat. A standard clock mechanism behind a panel with a square glass cutout.//

I was going to say that wouldn't work for the (shorter) hour hand. But you could do it /twice/.
And you don't really need the glass, just the square hole.
-- Loris, May 09 2021


The hands could be fixed, but the square frame could expand and contract so the minute hand always seemed to be the same distance from the edge
-- pocmloc, May 09 2021


If you made a series of gears that, at their circumference, contained other gears, which at their circumference, contained other gears...for the appropriate number of iterations (6 seems to be a minimum for a passable square), you should be able to construct a Fourier object that traced out a square (or any other shape, see links). From there, you could attach some black elastic back to the centre which would serve as the "hand". The tension would likely make this impractical, but it's worth mentioning just as an excuse to post a link to the Fourier stuff as a tangential thingy.
-- zen_tom, May 09 2021


A sweep second hand might move fast enough to see a pulsatile effect at continually varying second hand length.

Also the idea reminds me of square wheels [link].

There's something called a Haar wavelet that does what fourier does, but differently.
-- beanangel, May 09 2021


There are many mechanisms and ways to make the hands extend & retract; the trick will be squeezing it all into the (generally minimalist) hands & centre area of the clock.
-- neutrinos_shadow, May 10 2021


You could have the hour hand attached to a chain (or toothed belt) that runs around the perimeter of the square clock with small sprockets at each of the four corners. In this way the hour hand would almost always be vertical or horizontal (except when moving around the corners). Another chain and sprocket set behind (or in front of) the first set could have the minute hand.
-- xaviergisz, May 10 2021



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