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April 1

Where: $x$ indicates a variable, and $x 0$ indicates some fixed point, is the expression $(x-x 0)$ common in contexts other than Calculus and Analytic geometry?

In Calculus: the expression $(x-x_{0})$ is pretty common, e.g. when defining the derivative at $x_{0}$ as: $\lim _{x\to x_{0}}{\frac {f(x)-f(x_{0})}{x-x_{0}}},$ or when defining the graph of the tangent line passing through $x_{0}$ as: $y(x)=f(x_{0})+f'(x_{0})(x-x_{0}),$ and the like.

In Anaytic geometry: besides the graph of the tangent line (which is defined as mentioned above), the graph of the circle whose center is located at $(x_{0},y_{0})$ and whose radius is $r,$ is defined as: $y_{\pm }(x)=y_{0}\pm {\sqrt {r^{2}-(x-x_{0})^{2}}}$

I remember that this expression, $(x-x_{0}),$ is also common in some other contexts (i.e. other than Calculus and Analytic geometry) - whether mathematical or scientific ones, but I can't remember where. Can anyone remind me of them? 147.235.210.76 (talk) 07:06, 1 April 2025 (UTC)[reply]

One remark. The use of

0

as the subscript for the anchored variable is rather recent; in older texts we typically find

x-x_{1}

(or

t-t_{1}

if the variable represents time, and so on); see for example here or here. This is still quite common also in modern textbooks, as seen e.g. here.

You can expect expressions of this form in any context where the distance between a varying quantity and a fixed one is considered. Here on Wikipedia, for instance, you can see the expression in the last bullet point of Lorentz transformation § Coordinate transformation. The context in which you may have seen this is that of the defining expression for a Taylor series, as seen for example here. ‑‑Lambiam 09:51, 1 April 2025 (UTC)[reply]

As to Lorentz transformation, I haven't found. Could you quote any formula containing the expression

(x-x_{0})

or

(x-x_{1})?

As to Taylor series, it's a branch in Calculus, but I've asked about any context "other than Calculus" (and than Analytic geometry). See the header. 147.235.210.76 (talk) 10:08, 1 April 2025 (UTC)[reply]

if the coordinate systems are never coincident (i.e., not in standard configuration), and if both observers can agree on an event $t 0, x 0, y 0, z 0$ in $F$ and $t 0', x 0', y 0', z 0'$ in $F'$ , then they can use that event as the origin, and the spacetime coordinate differences are the differences between their coordinates and this origin, e.g., $Δ x = x - x 0$ , $Δ x' = x' - x 0'$ , etc.

‑‑Lambiam 11:33, 1 April 2025 (UTC)[reply]

All right, I'm taking your example of Taylor series, that may help me for asking a new question, in a new thread (see below). 147.235.210.76 (talk) 06:58, 2 April 2025 (UTC)[reply]

Does the operation of shifting a given point to the origin, have an accepted name?

E.g. shifting the center of circle, or shifting a point of tangency, or shifting a point of intersection, to the origin. 147.235.210.76 (talk) 09:47, 1 April 2025 (UTC)[reply]

Translation. ‑‑Lambiam 09:52, 1 April 2025 (UTC)[reply]

I've asked about shifting a given point to the origin. "Translation" is not necessarily to the origin. 147.235.210.76 (talk) 10:10, 1 April 2025 (UTC)[reply]

"Translation of a point to the origin." Not everything gets a special name, otherwise math jargon would be even harder than it already is. --RDBury (talk) 12:29, 1 April 2025 (UTC)[reply]

Any translation shifts some point to the origin. —Tamfang (talk) 00:56, 2 April 2025 (UTC)[reply]

Whereas the header points out: "a given point", as you have certainly noticed. 147.235.210.76 (talk) 05:33, 2 April 2025 (UTC)[reply]

Just moving a single point to the origin is not very meaningful. Presumably, you want to translate a pointed configuration so as to let its basepoint become the origin. ‑‑Lambiam 05:49, 2 April 2025 (UTC)[reply]

Let's assume I do. So does this kind of translation have an accepted name? 147.235.210.76 (talk) 06:41, 2 April 2025 (UTC)[reply]

I don't think so. Even if someone has invented a name for this, I expect most mathematicians will not know it. If everything of interest moves with the point, you might wish to describe the operation as a translational coordinate transformation instead of a translation. ‑‑Lambiam 13:42, 2 April 2025 (UTC)[reply]

Let's just call it zeroing and be done with it. --Wrongfilter (talk) 13:57, 2 April 2025 (UTC)[reply]

I asked about an "accepted name" (of the operation of shifting a given point to the origin). Is it? 147.235.210.76 (talk) 15:02, 2 April 2025 (UTC)[reply]

User:Lambiam just said "Even if someone has invented a name for this, I expect most mathematicians will not know it." The suggestion made by User:Wrongfilter is a perfect exemplar of this. Obviously, large sections of the global mathematical community watch the Wikipedia Mathematics Reference Desk religiously for news of major developments. But can we say that "zeroing" has become "accepted" by that community after only 28 hours? I think you know the answer to that. -- Jack of Oz ^{[pleasantries]} 17:56, 3 April 2025 (UTC)[reply]

I think this operation in this context is often called “recentering”. 100.36.106.199 (talk) 02:16, 7 April 2025 (UTC)[reply]

April 1

Where: x indicates a variable, and x0 indicates some fixed point, is the expression (x-x0) common in contexts other than Calculus and Analytic geometry?

Does the operation of shifting a given point to the origin, have an accepted name?

Where: $x$ indicates a variable, and $x 0$ indicates some fixed point, is the expression $(x-x 0)$ common in contexts other than Calculus and Analytic geometry?