What are the different types of constants in physics and math?

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Constants in physics and mathematics are fixed values that do not change, with distinctions made between physical science constants and mathematical constants. Physical constants can be universal, defined with specific units such as meters or seconds, while some are dimensionless, like the neutron-electron mass ratio. The numeric values of dimensioned constants depend on the defined units, which are themselves fixed. The discussion emphasizes that not all constants are equivalent, highlighting the complexity of their definitions and applications. Understanding these differences is crucial for interpreting equations that involve constants.
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I know a constant is a fixed number, but what is a constant exactly? What does it mean when you have an equation that equals a constant?

Ty
 
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As Sirus noted there are different kinds of constants, physical science versus mathematical constants.

There are official physical science constants defined as Universal at the following URL:
http://physics.nist.gov/cgi-bin/cuu/Category?view=html&Universal.x=82&Universal.y=7

It should be noted that the universal constants are dimensioned, that is, described using units which are themselves defined values (meters, seconds, temp., etc.). None of the physical science constants are "dimensioned" by a unit that is in itself a physical science constant.

There are a number of physical science constants that are dimensionless, usually ratios, like the neutron-electron mass ratio. The numeric value of dimensioned physical science constants are predicated upon the "value" of the defined units. I would say all constants are not created equal.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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