Confusion over the word “ratio” in the definition of $pi$
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According to Wikipedia, pi is "a mathematical constant that was originally defined as the ratio of a circle's circumference to its diameter."
However, when I think of the word "ratio", something like $4:3$ or $7:10$ comes to mind. Why is pi said to be a ratio? Isn't it more accurate to say that pi is the circumference divided by its diameter, rather than the ratio of the circumference to the diameter (which I would think of as $pi:1$)?
definition circle pi
edited Dec 6 '18 at 20:13
Blue
48k870153
asked Dec 6 '18 at 20:05
JoeJoe
111
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add a comment |
$begingroup$
According to Wikipedia, pi is "a mathematical constant that was originally defined as the ratio of a circle's circumference to its diameter."
However, when I think of the word "ratio", something like $4:3$ or $7:10$ comes to mind. Why is pi said to be a ratio? Isn't it more accurate to say that pi is the circumference divided by its diameter, rather than the ratio of the circumference to the diameter (which I would think of as $pi:1$)?
definition circle pi
edited Dec 6 '18 at 20:13
Blue
48k870153
asked Dec 6 '18 at 20:05
JoeJoe
111
$endgroup$
1
$begingroup$
divided by means ratio. In other words, $a/b$. Here $a$ is the circumference, and $b$ is the diameter. You cannot use $pi$ there already, because you want to define $pi$ this way. So, no, $pi=pi:1$ is not what you want.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 20:08
add a comment |
$begingroup$
According to Wikipedia, pi is "a mathematical constant that was originally defined as the ratio of a circle's circumference to its diameter."
However, when I think of the word "ratio", something like $4:3$ or $7:10$ comes to mind. Why is pi said to be a ratio? Isn't it more accurate to say that pi is the circumference divided by its diameter, rather than the ratio of the circumference to the diameter (which I would think of as $pi:1$)?
definition circle pi
edited Dec 6 '18 at 20:13
Blue
48k870153
asked Dec 6 '18 at 20:05
JoeJoe
111
$endgroup$
According to Wikipedia, pi is "a mathematical constant that was originally defined as the ratio of a circle's circumference to its diameter."
However, when I think of the word "ratio", something like $4:3$ or $7:10$ comes to mind. Why is pi said to be a ratio? Isn't it more accurate to say that pi is the circumference divided by its diameter, rather than the ratio of the circumference to the diameter (which I would think of as $pi:1$)?
definition circle pi
definition circle pi
edited Dec 6 '18 at 20:13
Blue
48k870153
asked Dec 6 '18 at 20:05
JoeJoe
111
edited Dec 6 '18 at 20:13
Blue
48k870153
asked Dec 6 '18 at 20:05
JoeJoe
111
edited Dec 6 '18 at 20:13
Blue
48k870153
edited Dec 6 '18 at 20:13
Blue
48k870153
edited Dec 6 '18 at 20:13
Blue
48k870153
48k870153
asked Dec 6 '18 at 20:05
JoeJoe
111
asked Dec 6 '18 at 20:05
JoeJoe
111
asked Dec 6 '18 at 20:05
JoeJoe
111
111
1
$begingroup$
divided by means ratio. In other words, $a/b$. Here $a$ is the circumference, and $b$ is the diameter. You cannot use $pi$ there already, because you want to define $pi$ this way. So, no, $pi=pi:1$ is not what you want.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 20:08
add a comment |
1
$begingroup$
divided by means ratio. In other words, $a/b$. Here $a$ is the circumference, and $b$ is the diameter. You cannot use $pi$ there already, because you want to define $pi$ this way. So, no, $pi=pi:1$ is not what you want.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 20:08
1
1
$begingroup$
divided by means ratio. In other words, $a/b$. Here $a$ is the circumference, and $b$ is the diameter. You cannot use $pi$ there already, because you want to define $pi$ this way. So, no, $pi=pi:1$ is not what you want.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 20:08
$begingroup$
divided by means ratio. In other words, $a/b$. Here $a$ is the circumference, and $b$ is the diameter. You cannot use $pi$ there already, because you want to define $pi$ this way. So, no, $pi=pi:1$ is not what you want.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 20:08
add a comment |
1 Answer
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$begingroup$
Recall that circumference of a circle is $C = pi d$, where $d$ is the diameter. Then, $$pi={Cover d},$$ as you mentioned. If we had the exact length of the circumference of the circle, and its diameter, then we will compute $pi$ exactly. However, as you learn in any science class, our instruments of measurement are not perfect and subject to roundoff error. So maybe using a ruler, you compute that your circle's circumference is $31$ inches, and its diameter is $10$ inches. Then $pi approx 31 div10=3.1$. If we can get a more precise measuring tool, we get closer to $pi=3.141592ldots$
answered Dec 6 '18 at 20:15
Decaf-MathDecaf-Math
3,254825
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$begingroup$
Recall that circumference of a circle is $C = pi d$, where $d$ is the diameter. Then, $$pi={Cover d},$$ as you mentioned. If we had the exact length of the circumference of the circle, and its diameter, then we will compute $pi$ exactly. However, as you learn in any science class, our instruments of measurement are not perfect and subject to roundoff error. So maybe using a ruler, you compute that your circle's circumference is $31$ inches, and its diameter is $10$ inches. Then $pi approx 31 div10=3.1$. If we can get a more precise measuring tool, we get closer to $pi=3.141592ldots$
answered Dec 6 '18 at 20:15
Decaf-MathDecaf-Math
3,254825
$endgroup$
add a comment |
$begingroup$
Recall that circumference of a circle is $C = pi d$, where $d$ is the diameter. Then, $$pi={Cover d},$$ as you mentioned. If we had the exact length of the circumference of the circle, and its diameter, then we will compute $pi$ exactly. However, as you learn in any science class, our instruments of measurement are not perfect and subject to roundoff error. So maybe using a ruler, you compute that your circle's circumference is $31$ inches, and its diameter is $10$ inches. Then $pi approx 31 div10=3.1$. If we can get a more precise measuring tool, we get closer to $pi=3.141592ldots$
answered Dec 6 '18 at 20:15
Decaf-MathDecaf-Math
3,254825
$endgroup$
add a comment |
$begingroup$
Recall that circumference of a circle is $C = pi d$, where $d$ is the diameter. Then, $$pi={Cover d},$$ as you mentioned. If we had the exact length of the circumference of the circle, and its diameter, then we will compute $pi$ exactly. However, as you learn in any science class, our instruments of measurement are not perfect and subject to roundoff error. So maybe using a ruler, you compute that your circle's circumference is $31$ inches, and its diameter is $10$ inches. Then $pi approx 31 div10=3.1$. If we can get a more precise measuring tool, we get closer to $pi=3.141592ldots$
answered Dec 6 '18 at 20:15
Decaf-MathDecaf-Math
3,254825
$endgroup$
Recall that circumference of a circle is $C = pi d$, where $d$ is the diameter. Then, $$pi={Cover d},$$ as you mentioned. If we had the exact length of the circumference of the circle, and its diameter, then we will compute $pi$ exactly. However, as you learn in any science class, our instruments of measurement are not perfect and subject to roundoff error. So maybe using a ruler, you compute that your circle's circumference is $31$ inches, and its diameter is $10$ inches. Then $pi approx 31 div10=3.1$. If we can get a more precise measuring tool, we get closer to $pi=3.141592ldots$
answered Dec 6 '18 at 20:15
Decaf-MathDecaf-Math
3,254825
answered Dec 6 '18 at 20:15
Decaf-MathDecaf-Math
3,254825
answered Dec 6 '18 at 20:15
Decaf-MathDecaf-Math
3,254825
answered Dec 6 '18 at 20:15
Decaf-MathDecaf-Math
3,254825
3,254825
add a comment |
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$begingroup$
divided by means ratio. In other words, $a/b$. Here $a$ is the circumference, and $b$ is the diameter. You cannot use $pi$ there already, because you want to define $pi$ this way. So, no, $pi=pi:1$ is not what you want.
$endgroup$
– Dietrich Burde
Dec 6 '18 at 20:08