When To Use $m$ Vs $\angle Abc$
In geometry problems, usually I see something like $\angle ABC=\dfrac$ when an angle needs to be given a measure. However, sometimes I see people write that same equation as $m=\dfrac$. What is the correct notation?
- 1$\begingroup$Whatever you agreed on? I personally have never seen the second so it might even mean something else for all I know, but as long as the reader knows what you mean it’s all good. In doubt, write the definition down so the reader definitely knows what you mean. Math is about the ideas and concepts, not about the language or notation you write it in.$\endgroup$Mar 17, 2018 at 21:31
- 1$\begingroup$Do you say $\angle ABC$ for the angle itself, or for the measure of the angle? Similarly, do you say $\overline$ for the line segment itself, or for the length of the line segment? Follow the notation used by those you are communicating with.$\endgroup$Mar 17, 2018 at 21:41
- $\begingroup$@GEdgar I use both notations for both$\endgroup$ ericw31415Mar 17, 2018 at 21:56
- $\begingroup$FYI: Some countries $m$ is used for slope of a straight line such as $y=mx+c$ where $c=$intercept, and $m=\tan\theta$ .$\endgroup$ Mathew MahindaratneMar 17, 2018 at 21:58
- $\begingroup$@MathewMahindaratne Yeah, but in different contexts, symbols mean different things, such as $\pi$ as a constant and $\pi$ for the prime-counting function.$\endgroup$
Geometry Notation: What Does $m\angle Abc$ Mean
I see in some math formulation that a certain angle is called, let’s say
$$\angle ABC$$
but there is a letter put in front of the angle notation.
$$m\angle ABC$$
- $\begingroup$Try to use LaTeX to write accurately mathematics here. You also didn’t write what the angle is called, “let say…”$\endgroup$Oct 30, 2013 at 17:23
- $\begingroup$< ABC and m< ABC.. I dont know why it doesnt show up in the question..$\endgroup$Oct 30, 2013 at 17:24
- $\begingroup$Do you mean $\theta$?$\endgroup$ Don LarynxOct 30, 2013 at 17:24
- $\begingroup$You’re going to give more context, for example to write down a complete exercise. The letter $\ m\ $ is many times reserved for slope in analytic geometry.$\endgroup$Oct 30, 2013 at 17:25
- 3$\begingroup$It’s because the < hides the subsequent text when the post is rendered. I have fixed it.$\endgroup$
$\angle ABC$ : The angle ABC
$m\angle ABC$: The measure of $\angle ABC$
So, when $\angle ABC \cong \angle DFG$ , that means, $m\angle ABC = m\angle DFG$
Or * Or Multiplication
These symbols have the same meaning commonly × is used to mean multiplication when handwritten or used on a calculator 2 × 2, for example.
The symbol * is used in spreadsheets and other computer applications to indicate a multiplication, although * does have other more complex meanings in mathematics.
Less commonly, multiplication may also be symbolised by a dot . or indeed by no symbol at all. For example, if you see a number written outside brackets with no operator , then it should be multiplied by the contents of the brackets: 2 is the same as 2×.
See our page on Multiplication for more.
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Common Symbols Used In Geometry
Symbols save time and space when writing. Here are the most common geometrical symbols:
Symbol | ||
---|---|---|
ABC has 3 equal sides | Triangle ABC has three equal sides | |
A right angle is 90 degrees | ||
Line Segment “AB” | The line segment between A and B | |
Line “AB” | The infinite line that includes A and B | |
Ray “AB” | The line that starts at A, goes through B and continues on | |
Congruent | ABC | Triangle ABC is congruent to triangle DEF |
Similar | DEF | Triangle DEF is similar to triangle MNO |
Therefore |
Why Is M A Symbol For Slope
Q: This drives math teachers crazy, perhaps because its more of a language question: Why do we use the letter m for the slope of a line? If you dont know, youre in good company. Even people on the Math Forum arent sure.
A: Were in good company, it seems, though we can clear up some of the nonsense found online about the use of m as a symbol for slope. Lets begin with a bit of history.
The CRC Concise Encyclopedia of Mathematics by Eric W. Weisstein says the letter m was first used in print as a symbol for slope in the mid-19th century.
Weisstein traces the usage to an 1844 treatise on geometry by the British mathematician Matthew OBrien.
That may be the earliest use of the symbol in an English work, but Sandro Caparrini, a scholar at the University of Torino in Italy, has traced the usage all the way back to a 1757 work by the Italian mathematician Vincenzo Riccati.
Why, you ask, did the letter m become the symbol for the slope of a line instead of, say, s or some other letter?
First, we ought to point out that the symbol is different in some other languages.
In Swedish, for example, its k. The mathematician Erland Gadde has speculated that the k stands for koefficient, which is part of a longer technical word for slope in Swedish.
But getting back to your question about the symbol m, one theory is that it comes from monter, which means to climb in French. Unfortunately, theres no evidence to support this.
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The Letter In Physics: Linear Density
Linear density is the degree of mass per unit length. The value is especially useful for measuring the weight of objects that appear to be one-dimensional, such as threads, strings, yarn and wires.
Linear density is represented mathematically as:
µ = mass/length
The SI unit of linear density is kg/m.
In addition to kg/m, another unit is also used to represent mass per unit length. This is known as the tex, which is the number of grams per 1,000 meters. Another unit is the denier, which is the number of grams per 9,000 meters of thread. In real-world applications, a denier is a measure of the thread weight and thus, the opacity or fineness of a material.
The Letter In Physics: Coefficient Of Friction
In physics, the letter is commonly used to represent the coefficient of friction and magnetic permeability.
The coefficient of friction refers to the ratio of the frictional force resisting the motion of two surfaces that are in contact to the normal force that’s pressing the two surfaces together. The frictional force and the motion of the object are in opposite directions.
Mathematically, the coefficient of friction is represented as:
= F/N
The coefficient of friction is dimensionless because both F and N are measured in units of force .
The value of is different for static friction and kinetic friction. In static friction, the object remains at rest until the force of static friction is removed. Also, the frictional force resists force applied to the object. In contrast, in kinetic friction, the frictional force resists the motion of an object.
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Common Mathematical Symbols And Terminology: Maths Glossary
Mathematical symbols and terminology can be confusing and can be a barrier to learning and understanding basic numeracy.
This page complements our numeracy skills pages and provides a quick glossary of common mathematical symbols and terminology with concise definitions.
Are we missing something? Get it touch to let us know.
What Does E Mean In Math
The letter E can have two different meaning in math, depending on whether it’s a capital E or a lowercase e. You usually see the capital E on a calculator, where it means to raise the number that comes after it to a power of 10. For example, 1E6 would stand for 1 × 106, or 1 million. Normally, the use of E is reserved for numbers that would be too long to be displayed on the calculator screen if they were written out longhand.
Mathematicians use the lowercase e for a much more interesting purpose to denote Euler’s number. This number, like , is an irrational number, because it has a non-recurring decimal that stretches to infinity. Like an irrational person, an irrational number seems to make no sense, but the number that e denotes doesn’t have to make sense to be useful. In fact, it’s one of the most useful numbers in mathematics.
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The Letter In Chemistry
In chemistry, µ refers to the elementary particles muon and antimuon. A muon is similar to an electron. However, its mass is about 207 times the mass of the electron. It is created when an electron collides with its antiparticle positron . The collision creates a , which subsequently forms the muon and its antiparticle, the antimuon.
A muon is represented as and the antimuon as +. In a two-dimensional representation where the x-axis represents space and the y-axis represents time, the positron and antimuon are shown as moving backward in time. In other words, these particles are shown as moving toward the past. Such diagrams are very useful to depict different types of particle interactions, particularly to visualize the effects of electromagnetic interactions between electrons and photons.
The Letter In Electrical And Electronic Engineering
In electrical and electronic engineering, µ represents the electric mobility of a charged elementary particle like an electron or proton. Mobility simply means the tendency of the charged particles to move. It is proportional to the net charge of the particle.
When a uniform electric field acts upon this charged particle, it will accelerate until it reaches a constant drift velocity. This phenomenon is represented mathematically as:
µ = Vd / E
Vd = Drift velocity
E = Electric field
The SI unit of the electrical mobility is m2/ V s. This phenomenon is the basis for electrostatic precipitation which is used to remove particles from exhaust gases on a large scale.
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The Letter In Physics: Magnetic Permeability
Magnetic permeability refers to the relative change in the magnetic field inside a material compared to the magnetizing field where the material is located.
It is represented mathematically as:
= B/H
B in this case is magnetic flux density established within the material. It depends on the concentration of magnetic field lines per unit cross-sectional area.
H is the magnetic field strength of the magnetizing field. The field is produced by the flow of electric current through a wire.
The designation 0 refers to the permeability of free space. It is also known as the permeability of vacuum and the magnetic constant. In SI units, 0 was earlier equal to 4 × 10-7 weber per ampere-meter. But with the redefinition of the ampere in 2019, 0 is no longer equal to this value so it must be determined by experimentation. The relative permeability of r is the ratio /0. In free space or a vacuum, this value is equal to 1. Like the coefficient of friction, r is also dimensionless.
Applications In The Social Sciences
Although the geometric mean has been relatively rare in computing social statistics, starting from 2010 the United Nations Human Development Index did switch to this mode of calculation, on the grounds that it better reflected the non-substitutable nature of the statistics being compiled and compared:
- The geometric mean decreases the level of substitutability between dimensions and at the same time ensures that a 1 percent decline in say life expectancy at birth has the same impact on the HDI as a 1 percent decline in education or income. Thus, as a basis for comparisons of achievements, this method is also more respectful of the intrinsic differences across the dimensions than a simple average.
Not all values used to compute the HDI are normalized some of them instead have the form }\right)/\left} . This makes the choice of the geometric mean less obvious than one would expect from the “Properties” section above.
The equally distributed welfare equivalent income associated with an Atkinson Index with an inequality aversion parameter of 1.0 is simply the geometric mean of incomes. For values other than one, the equivalent value is an Lp norm divided by the number of elements, with p equal to one minus the inequality aversion parameter.
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E In Scientific Notation And The Meaning Of 1e6
You don’t need a calculator to use E to express a number in scientific notation. You can simply let E stand for the base root of an exponent, but only when the base is 10. You wouldn’t use E to stand for base 8, 4 or any other base, especially if the base is Euler’s number, e.
When you use E in this way, you write the number xEy, where x is the first set of integers in the number and y is the exponent. For example, you would write the number 1 million as 1E6. In regular scientific notation, this is 1 × 106, or 1 followed by 6 zeros. Similarly 5 million would be 5E6, and 42,732 would be 4.27E4. When writing a number in scientific notation, whether you use E or not, you usually round to two decimal places.
< Less Than And > Greater Than
This symbol < means less than, for example 2 < 4 means that 2 is less than 4.
This symbol > means greater than, for example 4 > 2.
These symbols mean less than or equal to and greater than or equal to and are commonly used in algebra. In computer applications < = and > = are used.
These symbols are less common and mean much less than, or much greater than.
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The Letter In Thermodynamics
In thermodynamics, µ represents the chemical potential of a system or a component of a system. It refers to the chemical energy possessed by 1 mol of the substance. Another way to describe chemical potential is “the energy added to a system when a particle is added to it.”
Mathematically, chemical potential is represented as:
µ = Uc/N
When the chemical potential between two locations changes, it creates a chemical potential gradient. This forces the migration of the corresponding chemical species from the high chemical potential region to a lower chemical potential region.
The chemical potential µ can be associated with any type of substance including the following:
Where Does Euler’s Number E Come From
The number represented by e was discovered by mathematician Leonard Euler as a solution to a problem posed by another mathematician, Jacob Bernoulli, 50 years earlier. Bernoulli’s problem was a financial one.
Suppose you put $1,000 in a bank that pays 100% annual compound interest and leave it there for a year. You’ll have $2,000. Now suppose the interest rate is half that, but the bank pays it twice a year. At the end of a year, you’d have $2,250. Now suppose the bank paid only 8.33%, which is 1/12 of 100%, but paid it 12 times a year. At the end of the year, you’d have $2,613. The general equation for this progression is:
where r is 1 and n is the payment period.
It turns out that, as n approaches infinity, the result gets closer and closer to e, which is 2.7182818284 to 10 decimal places. This is how Euler discovered it. The maximum return you could get on an investment of $1,000 in one year would be $2,718.
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The Letter In Fluid Mechanics
In fluid mechanics, µ represents viscosity. Viscosity measures a fluid’s resistance to flow. This resistance is caused by shearing stress in the fluid as well as shearing stress between the fluid and its container.
Mathematically, viscosity is represented as the ratio of shearing stress to the rate of change of velocity .
Shearing stress =
Rate of change of velocity = dv/dy = v
dv/dy is the derivative of velocity with respect to distance y.
Viscosity = µ =
dv/dy
Definition Of The Summation Symbol
The symbol `\sum` indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern.
For example, the sum of the first 4 squared integers, `1^2+2^2+3^2+4^2,` follows a simple pattern: each term is of the form `i^2,` and we add up values from `i=1` to `i=4.` We can write the sum compactly with summation notation as \Similarly, \We don’t have to use $i$ for the index, we could use another variable, like $j$:\begin \sum_^2 \frac & = \frac + \frac + \frac + \frac + \frac\\& = 1 + \frac + \frac + \frac + \frac\end
In general, we define the sum as:\
Cite this as
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Geometric Mean Of A Continuous Function
The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth and varying growth in business the geometric mean of growth rates is known as the compound annual growth rate . The geometric mean of growth over periods yields the equivalent constant growth rate that would yield the same final amount.
Suppose an orange tree yields 100 oranges one year and then 180, 210 and 300 the following years, so the growth is 80%, 16.6666% and 42.8571% for each year respectively. Using the arithmetic mean calculates a average growth of 46.5079% . However, if we start with 100 oranges and let it grow 46.5079% each year, the result is 314 oranges, not 300, so the linear average over-states the year-on-year growth.
Instead, we can use the geometric mean. Growing with 80% corresponds to multiplying with 1.80, so we take the geometric mean of 1.80, 1.166666 and 1.428571, i.e. 1.80 1.442249 }\approx 1.442249} thus the “average” growth per year is 44.2249%. If we start with 100 oranges and let the number grow with 44.2249% each year, the result is 300 oranges.