All questions with tag [math: geometric-construction]


On Constructions by Marked Straightedge and Compass

Pierpont proved that a regular $n$-gon is constructible by (singly) marked straightedge and compass if and only if $n = k \, p_1 \cdots p_{s}$, where $k = 2^{a_1} 3^{a_2}$ for $a_i \geq 0$ and $p_i = 2^{b_1} 3^{b_2} + 1 > 3$ is prime with $b_i \geq 0$. It has been known since the time of Archimedes that a marked straightedge allows for an...
2022-07-25 17:47:10

Construct circle tangent to two lines

Given two line segments $ab$ and $cd$, I want to draw a circle tangent to both line segments and passing through points $c$ and $b$. Primitive operations available to me are: Draw a line between two points. Draw a perpendicular line passing through a point. Draw a line at a particular angle passing through a point. Construct a circle with a gi...
2022-07-25 17:16:08

Geometrical construction of the product on $\mathbb R$

Possible Duplicate: Representing the multiplication of two numbers on the real line Consider the real line in the plane. Suppose you are given the location of the point associated to $0$ and two oter points $a$ and $b$ on the line, it's strightforward to provide a geometric construction(*) that allows you to identify the point associated to $...
2022-07-25 07:42:57

Representing the multiplication of two numbers on the real line

There is a simple way to graphically represent positive numbers $x$ and $y$ multiplied using only a ruler and a compass: Just draw the rectangle with height $y$ in top of it side $x$ (or vice versa), like this But is there a way to draw the number $xy$ directly on the real line (i.e. not as an area on top of the real line) by using only some st...
2022-07-24 02:52:51

Geometric construction of logarithms

Can you attract a logarithmic range simply making use of some brilliant geometric construction? Or can it just be done making use of a real table of logarithms? (It is clearly unimportant to attract a straight range. It isn't tough to attract a range where the rooms in between tick marks increases at each action. Yet I can not consider a means ...
2022-07-24 02:52:40

Division of a line segment in the given ration internally

Before I state my problem description, would like to describe problem which was stated before my problem. So it is like this Given a line segment $AB$. You are required to divide it internally in the ratio $2 : 3$. steps for this problem is following Draw a ray $AC$ making an acute angle with $AB$. Starting with $A$, mark off 5 points...
2022-07-22 14:52:06

Constructible angles

What are the constructible angles? Wikipidia sais: The only angles of limited order that might be created beginning with 2 factors are those whose order is either a power of 2, or an item of a power of 2 and also a set of distinctive Fermat tops. I do not recognize the specific definition of this, does it claim that an angle is constructib...
2022-07-22 12:45:58

Making an angle of 10 degree and its multiple using compass?

We all recognize quite possibly just how to make an angle of 15 and also 45 level and also its numerous making use of compass. Can any person inform me just how to make an angle of 10 level and also its numerous making use of compass?
2022-07-19 22:43:38

What is the distance of the two parallel lines?

So there is: $$\begin{align} e: 5x-2y &= 10 \\ f: 5x-2y &= -19 \end{align} $$ where $e$ and also $f$ are identical lines. Inquiry : What is the range of both parallel lines?
2022-07-17 12:16:54

Did anyone ever build a mechanical device to take fifth roots, or solve general quintics?

This question is from a post from John Baez's blog on, among other things, geometrical constructions. I was hoping someone here might know the answer. In his post, Baez writes that Nowadays we realize that if you only have a straightedge, you can only solve linear equations. Adding a compass to your toolkit lets you also take square roots, so y...
2022-07-15 00:33:31

Can a line of π lengths be drawn with a compass and straight edge?

I've attracted 2 arbitrary factors on a 2 dimensional aircraft. If the range in between these 2 factors is one device, can a line of π devices be attracted making use of a compass and also straight side? Or, exists an evidence that reveals this is difficult?
2022-07-13 22:40:24

Having two points of a square and only a compass, how to find the remaining two?

I bear in mind existing a mathematical puzzle some years back that I still can not address. The trouble is specified as follows: We have 2 factors on an aircraft, and also making use of just a compass, just how do we locate various other 2 factors, to make sure that all 4 of them would certainly be vertices of a square? I'm not exactly sure wh...
2022-07-11 05:56:36

Geometric proof of existence of irrational numbers.

It is very easy, making use of just straightedge and also compass, to construct illogical sizes, exists a means to confirm, making use of just straightedge and also compass, that there are constructible sizes which are illogical? Ie a geometric evidence. And also is it feasible to construct an (never-ending) series of sensible sizes or location...
2022-07-10 04:57:35

Triangle given its three perpendicular bisectors and a point of an edge

Is it feasible to establish a triangular offered its 3 vertical bisectors (conference at a factor which will be the circumcenter) and also, claim, a factor of a side, or any kind of problem that can make the remedy one-of-a-kind, making use of compass and also straightedge? Certainly I can place a system of formulas, yet I'm seeking a visual pro...
2022-07-08 03:34:22

Constructing $\pi^2$ and e with straightedge and compass

Is there a means to construct 2 contours with lengthratios $\pi^2$, or 2 locations of proportion $\pi^2$, on an aircraft surface area, with a straightedge and also compass? And also is e = 2.71 feasible?
2022-07-08 02:56:37

Direct proof that $\pi$ is not constructible

Is there a straight evidence that $\pi$ is not constructible, that is, that making even the circle can not be done by regulation and also compass? Certainly, $\pi$ is not constructible due to the fact that it is transcendental therefore is not an origin of any kind of polynomial with sensible coefficients. Yet exists a straightforward straight...
2022-07-05 22:07:02

Find the angle between two lines using a compass and straight edge.

I've attracted 2 arbitrary, non - parallel, straight lines on an aircraft. They go across over, creating 2 angles, $a$ and also $b$, where ($a + b + a + b) = 1$ (or $360^\circ$) and also $a ≤ b$. (Making $a$ either the intense angle or an appropriate angle.) Making use of just a compass and also straight side, just how would certainly I locate ...
2022-07-04 14:34:33

Straightedge-only constructions

I recognize Poncelet - Steiner informs us that offered a circle and also its facility, straightedge alone amounts straightedge and also compass. My inquiry is, what can we construct with totally straightedge? We absolutely can not construct any kind of square origins in a limited variety of actions. Offered a sector of device size, is it feasibl...
2022-07-02 23:13:14

Construction of a regular pentagon

In Robert Dixon's Mathographics, a regular pentagon is constructed with straightedge and compass only. It is the pentagon $ABCDE$ pictured below. I am having trouble seeing why the central angles are all $72^\circ$, though. Can anyone provide the proof? Also, does anyone know who this construction is due to? I haven't seen it anywhere, other t...
2022-07-02 21:00:36

Can a regular heptagon be constructed using a compass, straightedge, and angle trisector?

Euclid has an enchanting compass with which he can trisect any kind of angle. Along with a normal compass and also a straightedge, can he construct a normal heptagon?
2022-07-01 16:22:59