OpenLLM-France/wikimedia huggingface dataset:
# Differential Geometry/Arc Length

The length of a vector function $f$ on an interval $[a,b]$ is defined as
    $\sup \left\{x{\Bigg |}t_{n}\in [a,b],t_{n}<t_{n+1},x=\sum _{k=1}^{n}{\Big |}f(t_{k})-f(t_{k-1}){\Big |}\right\}$
If this number is finite, then this function is rectifiable.
For continuously differentiable vector functions, the arc length of that vector function on the interval $[a,b]$ would be equal to $\int \limits _{a}^{b}\left|{\vec {f}}'(x)\right|dx$ .

## Proof

Consider a partition $a=t_{0}<t_{1}<\cdots <t_{n}=b$ , and call it $P_{n}$ . Let $P_{n+1}$ be the partition $P_{n}$ with an additional point, and let $\lim _{n\to \infty }\max\{t_{n}-t_{n-1}\}=0$ , and let $l_{n}$ be the arc length of the segments by joining the $f(x)$ of the vector function. By the mean value theorem, there exists in the nth partition a number $t_{n}'$ such that
    ${\sqrt {\sum _{i=1}^{3}{\Bigx_{i}(t_{n})-x_{i}(t_{n-1}){\Big )}^{2}}}=(t_{n}-t_{n-1}){\sqrt {\sum _{i=1}^{3}x_{i}'(t_{n}')}}$
Hence,
    $l_{n}=\sum _{j=1}^{n}{\sqrt {\sum _{i=1}^{3}{\Bigx_{i}(t_{j})-x_{i}(t_{j-1}){\Big )}^{2}}}=\sum _{j=1}^{n}(t_{j}-t_{j-1}){\sqrt {\sum _{i=1}^{3}x_{i}'(t_{j}')}}$
which is equal to
    $\sum _{j=1}^{n}(t_{j}-t_{j-1}){\sqrt {\sum _{i=1}^{3}x_{i}'(t_{j})}}+\sum _{j=1}^{n}(t_{j}-t_{j-1})\left({\sqrt {\sum _{i=1}^{3}x_{i}'(t_{j}')}}-{\sqrt {\sum _{i=1}^{3}x_{i}'(t_{j})}}\right)$
The amount
    ${\sqrt {\sum _{i=1}^{3}x_{i}'(t_{j}')}}-{\sqrt {\sum _{i=1}^{3}x_{i}'(t_{j})}}$
shall be denoted $d_{j}$ . Because of the triangle inequality,
    $d_{j}\leq {\sqrt {\sum _{i=1}^{3}(x_{i}'(t_{j}')-x_{i}'(t_{j}))^{2}}}\leq \sum _{i=1}^{3}{\Big |}x_{i}'(t_{j}')-x_{i}'(t_{j}){\Big |}$
Each component is at least once continuously differentiable. There exists thus for any $\varepsilon >0$ , there is a $\delta >0$ such that
    ${\Big |}x_{i}'(a)-x_{i}'(b){\Big |}<{\frac {\varepsilon }{3}}$ when $|a-b|<\delta$ .
Therefore, if $\max\{t_{n}-t_{n-1}\}<\delta$ then $d_{j}<\varepsilon$ , so that
    $\left|\sum _{j=1}^{n}(t_{n}-t_{n-1})\right|d_{j}<\varepsilon (b-a)$ which approaches 0 when n approaches infinity.
Thus, the amount
    $\sum _{j=1}^{n}(t_{j}-t_{j-1}){\sqrt {\sum _{i=1}^{3}x_{i}'(t_{j})}}+\sum _{j=1}^{n}(t_{j}-t_{j-1})\left({\sqrt {\sum _{i=1}^{3}x_{i}'(t_{j}')}}-{\sqrt {\sum _{i=1}^{3}x_{i}'(t_{j})}}\right)$
approaches the integral $\int \limits _{a}^{b}\left|{\vec {f}}'(x)\right|dx$ since the right term approaches 0.
If there is another parametric representation from $[a',b']$ , and one obtains another arc length, then
    $\int \limits _{a'}^{b'}{\sqrt {\sum _{i=1}^{3}\left({\frac {dx_{i}}{dt}}\right)^{2}}}\left|{\frac {dt}{dt'}}\right|dt'=\int \limits _{a'}^{b'}{\sqrt {\sum _{i=1}^{3}\left({\frac {dx_{i}}{dt'}}\right)^{2}}}dt'$
indicating that it is the same for any parametric representation.
The function $s(t)=\int \limits _{t_{0}}^{t}\left|{\vec {f}}'(x)\right|dx$ where $t_{0}$ is a constant is called the arc length parameter of the curve. Its derivative turns out to be ${\Big |}f'(x){\Big |}$ .
# Differential Geometry/Frenet-Serret Formulae

The derivatives of the vectors t, p, and b can be expressed as a linear combination of these vectors. The formulae for these expressions are called the Frenet-Serret Formulae. This is natural because t, p, and b form an orthogonal basis for a three-dimensional vector space.
Of course, we know already that ${\frac {dt}{ds}}=\kappa p$ and ${\frac {db}{ds}}=-\tau p$ so it remains to find ${\frac {dp}{ds}}$. First, we differentiate $p\cdot p=1$ to obtain ${\frac {dp}{ds}}\cdot p=0$ so it takes on the form ${\frac {dp}{ds}}=at+cb$. We take the dot product of this with t to obtain $a={\frac {dp}{ds}}\cdot t$. Taking the derivative of $p\cdot t=0$, we get ${\frac {dp}{ds}}\cdot t+p\cdot {\frac {dt}{ds}}=0$ or ${\frac {dp}{ds}}\cdot t=-p\cdot {\frac {dt}{ds}}=-\kappa p\cdot p=-\kappa$. Also, taking the dot product of ${\frac {dp}{ds}}=at+cb$ with b, we obtain $c={\frac {dp}{ds}}\cdot p$. Taking the derivative of $p\cdot b=0$, we get ${\frac {dp}{ds}}\cdot b=-p\cdot {\frac {db}{ds}}=\tau$. Thus, we arrive at the following expression for ${\frac {dp}{dt}}$:
${\frac {dp}{dt}}=-\kappa t+\tau b$.
This formula, combined with the previous two formulae, are together called the Frenet-Serret Formulae and they can be represented by a skew-symmetric matrix.
# Differential Geometry/Binormal Vector, Binormal Line, and Rectifying Plane

Consider a curve C of class of at least 2 with the arc length parametrization f(s).
The unit binormal vector is the cross product of the unit tangent vector and the unit principal normal vector,
$b(s)=t(s)\times p(s)$
which has a magnitude of 1 because t(s) and p(s) are orthogonal, and which are orthogonal to both t(s) and p(s).
The line passing through f(s) in the direction of b(s) is called the binormal line, and the plane spanned by the b(s) and t(s) is called the rectifying plane.
Now we have equations of the three planes. The normal plane is given by the equation $(x_{1}-f(s))\cdot t(s)=0$, the rectifying plane is given by the equation $(x_{1}-f(s))\cdot p(s)=0$, and the osculating plane is given by the equation $(x_{1}-f(s))\cdot b(s)=0$. It is easy to see that the earlier formula for the osculating plane is the same as this formula.
# Differential Geometry/Osculating Plane

The term osculating plane, which was first used by Tinseau in 1780, of a curve C parametrized by a function f(t) at a point f(a) is the plane that is approached when it is spanned by two vectors f(x)-f(a) and f(y)-f(a) when x and y both approach a.
First, assume that the curve C is at least of class 2.
Then consider the points $x$, $x+h_{1}$, and $x+h_{2}$ and consider the points $P=f(x)$, $P_{1}=f(x+h_{1})$, and $P_{2}=f(x+h_{2})$. The segments $PP_{1}$ and $PP_{2}$ are the vectors $s_{i}=f(x+h_{i})-f(x)$. If these vectors are linearly independent, then they span a plane.
We can divide each of those vectors by $h_{i}$, meaning that the plane is also spanned by the vectors $a_{i}={\frac {s_{i}}{h_{i}}}$.
We can also replace the second vector by $b={\frac {2(a_{2}-a_{1})}{h_{2}-h_{1}}}$ and it is easy to see that $a_{1}$ and w span the same plane as the original vectors.
Using Taylor's formula, we get
$f(x+h_{i})-f(x)=h_{i}f'(x)+{\frac {h_{i}}{2!}}f''(x)+o(h_{i}^{2})$.
This indicates that $a_{1}=f'(x)+{\frac {h_{1}}{2}}f''(x)+o(h_{1})$ and that $b=f''(x)+o(1)$
Thus, as both $h_{1}$ and $h_{2}$ approach 0, $a_{1}$ approaches f'(x) and $b$ approaches f(x). The osculating plane is consequently spanned by f'(x) and f(x), and consequently contains the tangent line.
Consider the position vector $x_{1}$ of any point on the osculating plane.
Then it is obvious that the following scalar triple product is equal to 0:
$|(x_{1}-f(x))f'(x)f''(x)|=0$.
The intersection of the osculating plane and the normal plane is called the principal normal line.
If it happens to be the case that f'(x) and f(x) are linearly dependent, then we can consider every plane containing the tangent line to be the osculating plane.
# Differential Geometry/Tangent Line, Unit Tangent Vector, and Normal Plane

The arc length can be used as a derivative for the vector function f, which is denoted t(x):
$t(x)={\frac {df(x)}{ds}}$.
Since
${\frac {df(x)}{ds}}={\frac {f'(x)}{s'(x)}}={\frac {f'(x)}{|f'(x)|}}$
which confirms the fact that it is a unit vector since the dot product with itself is 1. This also verifies a useful formula for the unit tangent vector
$t(x)={\frac {f'(x)}{|f'(x)|}}$.
The tangent line goes through f(x) and is spanned by the vector t(x). Thus, it is equal to the line spanned by
$f(x)+a{\frac {f'(x)}{|f'(x)|}}$
where a is any real number.
The normal plane at the point f(x) is the plane that is normal to the tangent line, and thus the unit tangent vector. Therefore, its equations is given by
$|z-f(x)|\cdot t(x)=0$
where z is any element of the surface, since it must be orthogonal.
# Differential Geometry/Curvature and Osculating Circle

Consider a curve $C$ of class of at least 2, parametrized by the arc length parameter, $f(s)$.
The magnitude of $f''(s)$ is called the curvature of the curve $C$ at the point $f(s)$. The multiplicative inverse of the curvature is called the radius of curvature.
The curvature is 0 at every point if and only if the curve is a straight line. Suppose that the curvature is always 0. Then $f''(s)$ is always 0, which proves that it is a straight line through elementary integrations.
We can also consider the normal vector $f''(s)$ to be the curvature vector.
The point that is away from $f(s)$ by a distance of the radius of curvature in the direction of the principal normal unit vector is called the center of curvature of the point $f(s)$ and the circle with the center on the center of curvature and with the radius as the radius of curvature is called the osculating circle at the point $f(s)$. It is very obvious that the unit tangent vector at the point $f(s)$ is tangent to the osculating circle at $f(s)$.
# Differential Geometry/Torsion

Consider a curve of class of at least 3, with a nonzero curvature.
We shall now consider the rate of change of the osculating plane. Of course, when the curve is a plane curve, the osculating plane is the same as the plane of the curve, so it does not change, and consequently, the binormal vector also does not change. In other words, the derivative of the binormal vector, ${\frac {db}{ds}}$, is 0.
Thus, let us consider the derivative of the binormal vector.
Consider the two equations $b\cdot b=1$ and $b\cdot t=0$ and differentiate both of them in respect to the arc length parameter, to obtain $b\cdot {\frac {db}{ds}}=0$ and ${\frac {db}{ds}}\cdot t+b\cdot {\frac {dt}{ds}}$ and consequently ${\frac {db}{ds}}\cdot t=-b\cdot {\frac {dt}{ds}}=-\kappa b\cdot p=0$ indicating that ${\frac {db}{ds}}$ is orthogonal to both b and p and thus lies on the principal normal line. Thus, we define the torsion $\tau (s)$ to be the proportionality between them:
${\frac {db}{ds}}(s)=-\tau (s)p(s)$
The negative sign is there so that it turns out that the torsion is positive for a right-handed helix.
We can take the dot product on both sides to get $\tau (s)=-p(s)\cdot {\frac {db}{ds}}(s)$
Its reciprocal, ${\frac {1}{\tau }}$ is called the radius of torsion.

## Exercises

* Prove that a curve is a plane curve if and only if its torsion is the null vector at every point.
# Differential Geometry
## Curves

* Chapter 1.1 Basic Concepts
* Chapter 1.2 Arc Length
* Chapter 1.3 Tangent Line, Unit Tangent Vector, and Normal Plane
* Chapter 1.4 Osculating Plane
* Chapter 1.5 Normal Line and Principal Unit Normal Vector
* Chapter 1.6 Curvature and Osculating Circle
* Chapter 1.7 Binormal Vector, Binormal Line, and Rectifying Plane
* Chapter 1.8 Torsion
* Chapter 1.9 Frenet-Serret Formulae
* Chapter 1.10 Vector of Darboux
* Chapter 1.11 Unit Spherical Indicatrices
* Chapter 1.12 Approximate Curves
* Chapter 1.13 Contact and Osculating Sphere
# Differential Geometry/Basic Concepts

Consider n functions, x$_1$(t), x$_2$(t), x$_3$(t), ..., x$_n$(t). Then consider the vector f function in R$^n$ which is given by f(t)=(x$_1$(t), x$_2$(t), x$_3$(t), ..., x$_n$(t)) is called a parametric representation of a set M, where M is the image of the function.
The point sets which shall be considered here must be able to be represented by a parametric representation (called an allowable parametric representation) f(t) where:
* The function f is continuously differentiable.
* The derivative f'(t) is different from the null vector for all t.
What is most important here are not individual parametric representations of vector function, but rather equivalence classes of vector functions which are have the same properties. These equivalences classes are called arcs.
Two of parametric representations f$_1$(x) and f$_2$(x) of a set are said to be equivalent if
* f$_1$$^{−1}$(f$_2$(t)) is defined on a closed interval [a,b].
* f$_1$$^{−1}$(f$_2$(t)) is continuously differentiable.
* f$_1$$^{−1}$(f$_2$(t))≠0 for all t in [a,b]
A point in a vector function f(t$_1$)=f(t$_2$) (t$_1$≠t$_2$) is called a multiple point. Arcs without multiple points are simple.
Arcs themselves are continuous as a vector function. Let $\epsilon >0$. Since each $x_{k}$ is continuous, there exists for each $k$ a $\delta _{k}$ such that
$\left|x_{k}(t_{1})-x_{k}(t_{2})\right|<{\frac {\epsilon }{\sqrt {n}}}\quad {\text{if}}\quad \left|t_{1}-t_{2}\right|<\delta _{k}$
Let δ = min{δ$_k$}. Then when |t$_1$-t$_2$|<ε, |f(t$_1$)-f(t$_2$)|=${\sqrt {\textstyle \sum _{k=1}^{n}(x_{k}(t_{1})-x_{k}(t_{2}))^{2}}}$<ε.
All simple arcs are thus homeomorphic to a segment.
Finally, curves are point sets representable by a arc such that for all functions within the arc, there is an interval whose image is the curve and such that any subinterval is an allowable parametric representation of some set.
A closed curve is one that is representable by a periodic function. All closed curves are homeomorphic to the circle.
# Differential Geometry/Normal Line and Principal Unit Normal Vector

Consider a curve C of class of at least 2 with the arc length parametrization f(s). The unit tangent vector is f'(s). Since f'(s)·f'(s)=1, we can differentiate this to obtain f'(s)·f(s)=0.
Therefore, if f(s) is not the zero vector, then it is a vector that is orthogonal to the unit tangent vector. The line passing through this vector and f(s) is the 'principal normal line of this curve at the point f(s). It is clear that this normal line is within the osculating plane because it is spanned by f(s). The unit vector within this line,
$p(s)={\frac {f''(s)}{|f''(s)|}}$,
is the unit principal normal vector of the curve C at the point f(s).
It is important to note that when you change the direction of the parametrization of the curve, the unit tangent vector also changes directions, but the principal normal unit vector does not.
# ERP Internals/Glossary/Overtime

If employees work more than eight hours per day, more than (typically) 40 hours per week or work on days they normally have off, they are paid overtime which is typically 1.5 (or sometimes 2.0) times their regular hourly rate.
# ERP Internals/Glossary/Packing Slip

A document prepared by the enterprise for use by the customer during receiving. Packing slips normally do not include prices.
# ERP Internals/Glossary/Password

A unique sequence of letters and numbers that identifies a user.
# ERP Internals/Glossary/Parts

An inventory item that can be is added to a component that will be sold to a customer. Contrast with Finished Good and Raw Material.
# ERP Internals/Glossary/Petty Cash

An amount of cash kept on hand to pay small expenses directly rather than going to the trouble of issuing an Accounts Payable check. Receipts are kept of each expense and periodically posted to the General Ledger.
# ERP Internals/Glossary/Postal Code

An identifier assigned by the Canadian Post Office for the purposes of delivering mail. "T2E 6O8" is a sample postal code. Contrast with Zip Code.
# ERP Internals/Glossary/Overdue

An invoice has a due date which is calculated using the invoice date and the terms. If the invoice is unpaid by the due date, it is overdue. Commonly, this term has the meaning of having been overdue for a significant period.
# ERP Internals/Glossary/Overhead

Indirect costs such as sales & marketing, administration and rent that must be allocated on some basis to jobs. This is in contrast to materials and labor which are associated with specific jobs.
# ERP Internals/Glossary/Physical Count

Once a year, every item is counted to correct errors that accumulated during the year. Contrast with Cycle Counting.
# ERP Internals/Glossary/Parameter

A piece of information that is relatively constant. For example, the company name is a parameter used by every module. Some parameters are used throughout the ERP; others are specific to one module. Some are maintained by Systems Administration and/or handled by Maintain Module Information. Contrast with Data Table.
# Embedded Systems/Serial and Parallel IO
## Data Transmission

Data can be sent either serially, one bit after another through a single wire, or in parallel, multiple bits at a time, through several parallel wires. Most famously, these different paradigms are visible in the form of the common PC ports "serial port" and "parallel port". Early parallel transmission schemes often were much faster than serial schemes (more wires = more data faster), but the added cost and complexity of hardware (more wires, more complicated transmitters and receivers). Serial data transmission is much more common in new communication protocols due to a reduction in the I/O pin count, hence a reduction in cost. Common serial protocols include SPI, and I$^2$C. Surprisingly, serial transmission methods can transmit at much higher clock rates per bit transmitted, thus tending to outweigh the primary advantage of parallel transmission. Parallel transmission protocols are now mainly reserved for applications like a CPU bus or between IC devices that are physically very close to each other, usually measured in just a few centimeters. Serial protocols are used for longer distance communication systems, ranging from shared external devices like a digital camera to global networks or even interplanetary communication for space probes, however some recent CPU bus architectures are even using serial methodologies as well.

## Serial Transmission
### RS-232
#### See Also

* Serial Programming Book

### RS-485
#### See also

* Serial Programming/RS-485

### I2C Inter-Integrated Circuit
#### See Also

I2C (Inter-Integrated Circuit) Bus Technical Overview and Frequently Asked Questions

### Ethernet

As on-chip memory increases, it is becoming more common to see Ethernet support in small system-on-chip embedded systems. New Ethernet ASIC products are also on the market. This allows an embedded system to have its own IP address on a network or on the internet. It can act as a server for its own webpage, to implement a GUI or general purpose I/O, and to display any relevant information such as sensor data, or even as a portal to remotely upgrade firmware. For example, many network routers have these features.

### USB
#### See Also

* Serial Programming/USB (Currently, Q1/2006, the module is a stub)

### Serial ATA
#### See Also

* Serial Programming/Serial ATA (Currently, Q1/2006, the module is a stub)

## Parallel Transmission
### Centronics

Centronics is synonymous with the 1980's PC standard parallel printer interface.

### ATA
## External links
## For further reading

* Robotics/Computer Control/The Interface/Networks
This page of the Embedded Systems book is a stub. You can help by expanding this section.
# Embedded Systems/Terminate and Stay Resident

In the original DOS operating system, there was no capability for multi-threading, or multi-process mechanisms. However, it was found to be very beneficial to leave certain components in memory even after the process that created it ended. These program fragments were known as Terminate and Stay Resident modules, and were the precursors to the dynamic library infrastructure of current Windows operating systems. TSR routines are often used to implement device drivers, or common library functions.
# Embedded Systems/Protected Mode and Real Mode
## x86 Processor Modes

Real mode and protected mode are two operating modes of the Intel x86 processor. However, there are certain other modes as well.

### V86 (Virtual 86 mode)

    This is the mode in which DOS applications run on Windows machine. This was done mainly to maintain compatibility with older DOS applications.

### SMM (System Management Mode)

    This mode was introduced, as the name suggests, for managing the system transparently without applications or OS getting the hint of it. Its primarily meant to be used by the BIOS code.

### Big Real Mode

    Now this mode is more like Real mode, but in this we can access full 4Gb address space of the 32-bit processor.

## Real Mode

This is the only mode which was supported by the 8086 (the very first processor of the x86 series). The 8086 had 20 address lines, so it was capable of addressing "2 raised to the power 20" i.e. 1 MB of memory.

## Protected Mode

This is the mode used most commonly by modern 32-bit operating systems.

## Entering Protected Mode

For instructions to enter protected mode, see: X86 Assembly/Protected Mode.
# Embedded Systems/Resources
## Wikimedia Resources

* Robotics
* Communication Systems
* Digital Signal Processing
* List of emulators
* Wikiversity:Embedded System Engineering
* Serial Programming Book
* Programmable Logic
* Parallel Computing and Computer Clusters
* Electric Circuits
* Analog and Digital Conversion
* Embedded Control Systems Design
* Digital Circuits
* Programmable Logic
* VHDL for FPGA Design

### Related Programming Resources

* Ada Programming
* Assembly Language
* C Programming
* C++ Programming
* Forth
* Software Engineers Handbook
* https://docs.rust-embedded.org/book/

## Web Resources

* "AN887: Microcontrollers made easy" 2002 a gentle introduction to microcontrollers in general and some of the things they do, with lots of pictures.
* Knowledge and concepts behind VLSI chip design
* Embedded System description in simple words
* Microcontrollers Forum
* http://www.EmbeddedRelated.com/
* Embedded White Papers, Downloads, Companies, News, Articles
* Microcontroller based free projects.
* Embedded Systems Design Magazine has articles such as "The basics of programming embedded processors: Part 1" by Wayne Wolf
* Embedded Systems Resources
* Electronics Components Tutorials for Robotics
* Dedicated Systems Magazine
* RTC Magazine
* COTS Journal
* Portable Design Magazine
* PKG Magazine
* www.embeddedcommunity.com
* "Tools for Embedded Developers" recommended by the Ganssle Group
* Embedded System News
* Embedded Systems Weekly
* "Technical Report on C++ Performance" by Dave Abrahams et al. has a lot of tips for using C++ in embedded systems.

## Books

The article "Turn a kid on to embedded systems" by Jack Ganssle 2005 recommends these books:
* "MC68HC05 Family, Understanding Small Microcontrollers" free download from Freescale "a well-written 300+ page tome that I highly recommend."
* "Ham Radio for Dummies" by Ward Silver 2004.
* the "ARRL Handbook" published by the American Radio Relay League.
* the "Engineer's Mini-Notebook for the 555 Timer." 32 pages by Forrest Mims III
* "Getting Started in Electronics" by Forrest Mims III ... "a 128-page complete intro to the field ... available from W5YI.org"
* "The Art of Electronics" by Horowitz and Hill. "For advanced tech wannabees only."
* "An Embedded Software Primer" by David Simon "the best introduction to writing firmware available."
* "Embedded Systems Design Using the Rabbit 3000 Microprocessor" by Kamal Hyder and Bob Perrin.
Other books about embedded systems:
* Barr, Michael et al. "Embedded Systems Dictionary" ISBN 1578201209
* Predko, Myke. "Programming and Customizing PICmicro Microcontrollers", McGraw Hill, 2002. ISBN 0071361723
* Pont, Michael J. "Embedded C" Addison Wesley, 2002. ISBN 020179523X
* Berger, Arnold S. "Embedded Systems Design: An Introduction to Processes, Tools and Techniques" CMP Books, 2001. ISBN 1578200733
# English as an Additional Language/Introducing verbs

Every subject in a sentence must have a verb. There are two types of verb in English:
* Active verbs
* Stative verbs

## Examples of Active Verbs

play, give, take, do, make, sing, sit, stand, eat, drink, sleep, walk, go

## Examples of Stative Verbs

be, like, hate, enjoy, see, want, love
# English as an Additional Language/Negatives

English forms negatives in the Simple Present using not.
The verb to be is special. Here is the negative form for it.
* I am from Canada. - I am not from Canada.
* She is from Finland. - She is not from Finland.
* She is from Finland. - She isn't from Finland
* She is from Finland. - She's not from Finland.
All other verbs use don't (do not) or doesn't (does not) to form negatives:
* I play football. - I do not play football.
* I play football. - I don't play football.
* She likes jazz. - She does not like jazz.
* She likes jazz. - She doesn't like jazz.