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Is it possible to geometrically construct any given real number? [closed]
Is $e$ “constructable” with the appropriate tools?Find a complex number geometricallyHow to construct geometrically $sqrt[k]n$ for $k in mathbbZ$ and $k>2$Minimal number of steps to construct $cos(2 pi /n)$Is $e$ “constructable” with the appropriate tools?How to raise a number to a power geometrically.Is it possible to represent imaginary and complex areas geometrically?Another way of proving sqrt 2 is a Real numberHow to draw triangle in plane using Peaucellier inversor?Constructing a complex number geometrically, without putting it in standard form.What is the essential difference between real number and complex number?
$begingroup$
I know some real numbers, like sqrt(2) can be constructed geometrically. But what about other real numbers, like 'e'? Is it possible to geometrically construct any given real number?
geometry analysis
asked May 5 at 12:16
user15740user15740
1141
$endgroup$
closed as too broad by YuiTo Cheng, RRL, Yanior Weg, Cesareo, mrtaurho May 7 at 13:43
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
I know some real numbers, like sqrt(2) can be constructed geometrically. But what about other real numbers, like 'e'? Is it possible to geometrically construct any given real number?
geometry analysis
asked May 5 at 12:16
user15740user15740
1141
$endgroup$
closed as too broad by YuiTo Cheng, RRL, Yanior Weg, Cesareo, mrtaurho May 7 at 13:43
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
See this question for a discussion of whether $e$ is constructible by means other than what I mentioned.
$endgroup$
– 雨が好きな人
May 5 at 12:23
$begingroup$
You should be precise about the meaning of "geometric construction". With a compass and (unmarked) strightedge even $sqrt[3]2$ is not constructible.
$endgroup$
– user
May 5 at 12:32
add a comment |
$begingroup$
I know some real numbers, like sqrt(2) can be constructed geometrically. But what about other real numbers, like 'e'? Is it possible to geometrically construct any given real number?
geometry analysis
asked May 5 at 12:16
user15740user15740
1141
$endgroup$
I know some real numbers, like sqrt(2) can be constructed geometrically. But what about other real numbers, like 'e'? Is it possible to geometrically construct any given real number?
geometry analysis
geometry analysis
asked May 5 at 12:16
user15740user15740
1141
asked May 5 at 12:16
user15740user15740
1141
asked May 5 at 12:16
user15740user15740
1141
asked May 5 at 12:16
user15740user15740
1141
asked May 5 at 12:16
user15740user15740
1141
1141
closed as too broad by YuiTo Cheng, RRL, Yanior Weg, Cesareo, mrtaurho May 7 at 13:43
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as too broad by YuiTo Cheng, RRL, Yanior Weg, Cesareo, mrtaurho May 7 at 13:43
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
See this question for a discussion of whether $e$ is constructible by means other than what I mentioned.
$endgroup$
– 雨が好きな人
May 5 at 12:23
$begingroup$
You should be precise about the meaning of "geometric construction". With a compass and (unmarked) strightedge even $sqrt[3]2$ is not constructible.
$endgroup$
– user
May 5 at 12:32
add a comment |
$begingroup$
See this question for a discussion of whether $e$ is constructible by means other than what I mentioned.
$endgroup$
– 雨が好きな人
May 5 at 12:23
$begingroup$
You should be precise about the meaning of "geometric construction". With a compass and (unmarked) strightedge even $sqrt[3]2$ is not constructible.
$endgroup$
– user
May 5 at 12:32
$begingroup$
See this question for a discussion of whether $e$ is constructible by means other than what I mentioned.
$endgroup$
– 雨が好きな人
May 5 at 12:23
$begingroup$
See this question for a discussion of whether $e$ is constructible by means other than what I mentioned.
$endgroup$
– 雨が好きな人
May 5 at 12:23
$begingroup$
You should be precise about the meaning of "geometric construction". With a compass and (unmarked) strightedge even $sqrt[3]2$ is not constructible.
$endgroup$
– user
May 5 at 12:32
$begingroup$
You should be precise about the meaning of "geometric construction". With a compass and (unmarked) strightedge even $sqrt[3]2$ is not constructible.
$endgroup$
– user
May 5 at 12:32
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
No, it is not possible if you are only using a compass and straightedge. See constructible numbers.
$sqrt2$ can be constructed, as you say, but there are other real numbers such as $e$ that cannot. The ancient problem of squaring the circle is impossible precisely because $sqrtpi$ is not a constructible number.
answered May 5 at 12:19
雨が好きな人雨が好きな人
2,097317
$endgroup$
add a comment |
$begingroup$
The set of constructable numbers is the same as the closure of Z to ÷ and sqrt(). That is, you can construct ratios of two given lengths, and you can convert any given rectangle to a square.
For the polygons, a polygon n can be constructed if the euler totient ø(n) is a power of 2. This means 2^x . 3. 5. 17. 257. 65537.
answered May 5 at 12:32
wendy.kriegerwendy.krieger
5,89311427
$endgroup$
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
No, it is not possible if you are only using a compass and straightedge. See constructible numbers.
$sqrt2$ can be constructed, as you say, but there are other real numbers such as $e$ that cannot. The ancient problem of squaring the circle is impossible precisely because $sqrtpi$ is not a constructible number.
answered May 5 at 12:19
雨が好きな人雨が好きな人
2,097317
$endgroup$
add a comment |
$begingroup$
No, it is not possible if you are only using a compass and straightedge. See constructible numbers.
$sqrt2$ can be constructed, as you say, but there are other real numbers such as $e$ that cannot. The ancient problem of squaring the circle is impossible precisely because $sqrtpi$ is not a constructible number.
answered May 5 at 12:19
雨が好きな人雨が好きな人
2,097317
$endgroup$
add a comment |
$begingroup$
No, it is not possible if you are only using a compass and straightedge. See constructible numbers.
$sqrt2$ can be constructed, as you say, but there are other real numbers such as $e$ that cannot. The ancient problem of squaring the circle is impossible precisely because $sqrtpi$ is not a constructible number.
answered May 5 at 12:19
雨が好きな人雨が好きな人
2,097317
$endgroup$
No, it is not possible if you are only using a compass and straightedge. See constructible numbers.
$sqrt2$ can be constructed, as you say, but there are other real numbers such as $e$ that cannot. The ancient problem of squaring the circle is impossible precisely because $sqrtpi$ is not a constructible number.
answered May 5 at 12:19
雨が好きな人雨が好きな人
2,097317
edited May 5 at 12:24
answered May 5 at 12:19
雨が好きな人雨が好きな人
2,097317
answered May 5 at 12:19
雨が好きな人雨が好きな人
2,097317
answered May 5 at 12:19
雨が好きな人雨が好きな人
2,097317
2,097317
add a comment |
add a comment |
$begingroup$
The set of constructable numbers is the same as the closure of Z to ÷ and sqrt(). That is, you can construct ratios of two given lengths, and you can convert any given rectangle to a square.
For the polygons, a polygon n can be constructed if the euler totient ø(n) is a power of 2. This means 2^x . 3. 5. 17. 257. 65537.
answered May 5 at 12:32
wendy.kriegerwendy.krieger
5,89311427
$endgroup$
add a comment |
$begingroup$
The set of constructable numbers is the same as the closure of Z to ÷ and sqrt(). That is, you can construct ratios of two given lengths, and you can convert any given rectangle to a square.
For the polygons, a polygon n can be constructed if the euler totient ø(n) is a power of 2. This means 2^x . 3. 5. 17. 257. 65537.
answered May 5 at 12:32
wendy.kriegerwendy.krieger
5,89311427
$endgroup$
add a comment |
$begingroup$
The set of constructable numbers is the same as the closure of Z to ÷ and sqrt(). That is, you can construct ratios of two given lengths, and you can convert any given rectangle to a square.
For the polygons, a polygon n can be constructed if the euler totient ø(n) is a power of 2. This means 2^x . 3. 5. 17. 257. 65537.
answered May 5 at 12:32
wendy.kriegerwendy.krieger
5,89311427
$endgroup$
The set of constructable numbers is the same as the closure of Z to ÷ and sqrt(). That is, you can construct ratios of two given lengths, and you can convert any given rectangle to a square.
For the polygons, a polygon n can be constructed if the euler totient ø(n) is a power of 2. This means 2^x . 3. 5. 17. 257. 65537.
answered May 5 at 12:32
wendy.kriegerwendy.krieger
5,89311427
answered May 5 at 12:32
wendy.kriegerwendy.krieger
5,89311427
answered May 5 at 12:32
wendy.kriegerwendy.krieger
5,89311427
answered May 5 at 12:32
wendy.kriegerwendy.krieger
5,89311427
5,89311427
add a comment |
add a comment |
$begingroup$
See this question for a discussion of whether $e$ is constructible by means other than what I mentioned.
$endgroup$
– 雨が好きな人
May 5 at 12:23
$begingroup$
You should be precise about the meaning of "geometric construction". With a compass and (unmarked) strightedge even $sqrt[3]2$ is not constructible.
$endgroup$
– user
May 5 at 12:32