# Questions tagged [geometric-interpretation]

Questions about understanding a problem geometrically.

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### Geometric effects of parameters in homogeneous second-order ordinary differential equations with constant coefficients

In homogeneous second-order ordinary differential equations (ODE) with constant coefficients, of the form: $$ay''+by'+cy=0,$$ is there any conclusion about the effects of ...
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### Why doesn't a line passing through origin satisfy the 2 intercept form of the equation of a straight line?

The 2 intercept form of an equation of a straight line, is: x/a + y/b = 1 Where, a and b are the x and y intercepts respectively. For a line passing through origin, these two intercepts will become 0, ...
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1 answer
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### Geometric interpretation of the non-uniqueness of the solution of a system of linear equations

Show that the equation $$\pmatrix{3&-7&0\\2&2&5\\1&3&4}\pmatrix{x\\y\\z} = \pmatrix{3\\2\\1}$$ does not have a unique solution, and give a geometrical interpretation. Now, the ...
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3 answers
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### What is the Point, and Meaning, of the Mean Value of a Function?

Ok, so I know that the mean value of a function, $f(x)$, on the interval $[a,b]$ is given by (or defined by?) $$\frac{1}{b-a}\int_a^bf(x)~dx$$ but I have $2$ basic questions about this: $1$: From a ...
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### Where is the "Interior" of a Clifford Torus

[I do not believe I have tagged this entirely correctly, feel free to change them.] In the case of spheres there is a related structure called a ball which based on its definition I visualise as being ...
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1 answer
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### What it is the interpretation of the below picture in set theory?

somone sent me the below picture and He asked me to give him its interpretation regarding set theory ? but I ask alos about its geometricall interpretation ?
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### Examples about Cohen-Macaulay property of rings and book recommendation on intuition

My professor asks me to give an example about a local non-CM rings that are CM after modding out at any minimal prime. After a while failing to do so, I believe it is impossible since there exists a ...