Confusion over the word “ratio” in the definition of $pi$
$begingroup$
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
47.8k870152
asked Dec 6 '18 at 20:05
JoeJoe
111
$endgroup$
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
47.8k870152
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
47.8k870152
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
47.8k870152
asked Dec 6 '18 at 20:05
JoeJoe
111
edited Dec 6 '18 at 20:13
Blue
47.8k870152
asked Dec 6 '18 at 20:05
JoeJoe
111
edited Dec 6 '18 at 20:13
Blue
47.8k870152
edited Dec 6 '18 at 20:13
Blue
47.8k870152
edited Dec 6 '18 at 20:13
Blue
47.8k870152
47.8k870152
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
1
active
oldest
votes
$begingroup$
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
3,234825
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3028978%2fconfusion-over-the-word-ratio-in-the-definition-of-pi%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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
3,234825
$endgroup$
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
3,234825
$endgroup$
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
3,234825
$endgroup$
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
3,234825
answered Dec 6 '18 at 20:15
Decaf-MathDecaf-Math
3,234825
answered Dec 6 '18 at 20:15
Decaf-MathDecaf-Math
3,234825
answered Dec 6 '18 at 20:15
Decaf-MathDecaf-Math
3,234825
3,234825
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3028978%2fconfusion-over-the-word-ratio-in-the-definition-of-pi%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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