3 ms·
It's sad this didn't catch on. It's particularly handy when you move to "square unos" (like "square millimeters" but dimensionless). For example, in microchip
by KirillPanov 5y ago
It's sad this didn't catch on. It's particularly handy when you move to "square unos" (like "square millimeters" but dimensionless).
For example, in microchips the sheet resistance of layers (metal, poly, etc) has units of "ohms per square uno". This is because a 1mm*10mm sheet and a 10mm*100mm sheet both have the same resistance (along the first axis). The latter sheet is longer (higher resistance) but wider (lower resistance) and the effects cancel out. So it's really "ohms per width-to-length-ratio", but width-to-length-ratio is a unitless quantity (mm per mm = mm/mm = uno).
Everybody call this "ohms per square". Frankly that just sounds weird, and grammatically invalid. Ohms per square what? Parse error. Before I heard about unos I would occasionally call it "ohms per aspect ratio" but I'm probably the only person who uses that terminology.
https://en.wikipedia.org/wiki/Sheet_resistance#Units https://en.wikipedia.org/wiki/Sheet_resistance#Units
- jonsen 5y agoI think ‘ohms per square’ is fine. Just like e.g. ‘seconds per radian’ is much better than ‘seconds per uno’. Uno is generic and tells nothing about the context.
- KirillPanov 5y agoIn this case it would be "ohms per square uno", not "ohms per uno". It's got all the same context as "ohms per square". In fact it has all the same words! Also radians are not unitless; they are fractional cycles, not ratios.
- jonsen 5y agoAs another commenter said, a square is a unit of the plane; a square figure; all sides equal. Likewise a radian is a unit of the plane; a pie-slice figure with all sides equal.
- KirillPanov 5y agoPie-wedge-shaped things are not the only use for radians. The phase [1] across a Josephson Junction is measured in radians, but there are no planes involved. The progress of a longitudinal wave [2] as seen passing a stationary observer is measured in radians per second, yet no plane is involved -- it works just fine in a one-dimensional universe. Radians measure cycles. If you limit yourself to geometry then sure, radians seem like a thing for measuring circles. But that's just a side effect of the fact that the only cyclic symmetries of Euclidean space are rotations. So the only cycles you're going to find in high school geometry will be related to circles. [1] https://en.wikipedia.org/wiki/Josephson_phase#The_Josephson_equations https://en.wikipedia.org/wiki/Josephson_phase#The_Josephson_... [2] https://en.wikipedia.org/wiki/Longitudinal_wave https://en.wikipedia.org/wiki/Longitudinal_wave
- HPsquared 5y agoReading the Wiki link, it seems "square" isn't referring to squaring a quantity, but a square geometry (i.e. the special case where width=length) - very different things.
- KirillPanov 5y agoThose are two sides of the same coin. It isn't pure coincidence that "square millimeters" and "square polygon" share the word "square".