Why is pie unitless

Also, the "why meter is not dimensionless? But I can tell the same for degree, isn't it? Add a comment. Active Oldest Votes. If we made both cycles and radians "dimensionless", i. But semantically , there is huge conceptual difference between e. Writing the 'rad' explicitely adds clarity and helps express the author's intend. It again is a matter of convention. Graham Kemp Graham Kemp k 6 6 gold badges 45 45 silver badges bronze badges. It is a dimensionless number multiplied by an arbitrarily chosen constant.

The preferred form of a dimensionless unit is 1 of something divided by 1 of something else. However length is not so. Pockets Pockets 3 3 silver badges 11 11 bronze badges. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Linked Related 2.

Hot Network Questions. Question feed. Mathematics Stack Exchange works best with JavaScript enabled. The point here is that types can be invented to avoid errors, just like with non-negative integers and non- null references.

These features aren't actually necessary , just they offer type-checking protection. And that's one of the nice things we get from units, which are largely a typing logic. And even if we omitted that qualifier, that " Watt "-qualifier helps to avoid mistaking the figure for some other sort of quantity.

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Active 1 year, 9 months ago. Viewed times. Add a comment. Active Oldest Votes. Joules since they are conceptually different. My favourite example: you'd rather describe the power collected in sunlight per unit area by a solar panel in Watts per square metre, not kilograms per cubic second.

Show 1 more comment. So it is for the radian, just to clear that you are speaking of degrees, etc. G Cab G Cab It also goes on to talk about commensurable quantities. Units could be removed from everything. We don't need to use units. Like, at all, ever. Units can be added to most anything. That's just one way of doing it! Ideally, unit logic should be kept simple. Tangential: Connection to type theory.

There're also " unsigned " variants that can't store negative values. In short, further qualifying units is like using stronger typing in programming. Nondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution of variables. For example, if a system has an intrinsic resonance frequency, length, or time constant, nondimensionalization can recover these values.

These are: 1-It is easier to recognize when to apply familiar mathermatical techniques. Begin typing your search term above and press enter to search. Press ESC to cancel. Skip to content Home Physics Is Pi a dimensionless constant?

Ben Davis October 22,