Recent questions in Postulates

Elementary geometryAnswered question

hangobw6h 2023-03-24

If two parallel lines are cut by a transversal, then:

each pair of alternate angles are equal

each pair of alternate angles add up to 180 degrees

each pair of corresponding angles add up to 180 degees.

each pair of corresponding angles is equal.

each pair of alternate angles are equal

each pair of alternate angles add up to 180 degrees

each pair of corresponding angles add up to 180 degees.

each pair of corresponding angles is equal.

Elementary geometryAnswered question

e2t1rek7cav 2023-03-22

The opposite faces of a dice always have a total of ___ on them.

Elementary geometryAnswered question

Beau Mckee 2023-03-08

What is the greatest number of acute angles that a triangle can contain?

Elementary geometryAnswered question

Jasiah Carlson 2023-02-28

When two lines cross each other at a point we call them ___ lines.

Elementary geometryAnswered question

aqkuax86xp0o 2023-02-25

Can you draw a line of length 2.25 centimetres using a ruler? How about using ruler and compass?

Elementary geometryAnswered question

Dorstadt4uz 2022-12-20

Help find out сan a triangle have two obtuse angle?

Elementary geometryAnswered question

Adriel Vance 2022-12-04

Parallel lines have no solution. True or false

Elementary geometryAnswered question

Will Osborn 2022-12-04

A line which intersects two or more lines on the same plane is called a

parallel

perpendicular

transversal

parallel

perpendicular

transversal

Elementary geometryAnswered question

vogarsfN8 2022-11-27

A __ is a flat surface in geometry that never ends in two dimensions and has no thickness. A point, a line, a plane, a circle

Elementary geometryAnswered question

Goundoubuf 2022-11-25

Logarithms and ratios.

This is the question:

${\mathrm{log}}_{b}64=\frac{3}{b}$

And have to find b.

So I tried a bit and got this:

$\frac{b}{\mathrm{log}b}=\frac{\mathrm{log}64}{3}$

But have no idea what to do next.

Thanks for your help.

This is the question:

${\mathrm{log}}_{b}64=\frac{3}{b}$

And have to find b.

So I tried a bit and got this:

$\frac{b}{\mathrm{log}b}=\frac{\mathrm{log}64}{3}$

But have no idea what to do next.

Thanks for your help.

Elementary geometryAnswered question

Jamir Summers 2022-11-25

What is the slope of a line parallel to the $y$-axis?

Elementary geometryAnswered question

linnibell17591 2022-11-04

When reading about the history of Euclid's Elements, one finds a pretty length story about the Greeks and Arabs spending countless hours trying to prove Euclid's 5th Postulate.

But I've yet to come across a source stating that "this is the man who finally proved the 5th postulate!"

Has it ever been formally proven, or am I misunderstanding the issue?

But I've yet to come across a source stating that "this is the man who finally proved the 5th postulate!"

Has it ever been formally proven, or am I misunderstanding the issue?

Elementary geometryAnswered question

miniliv4 2022-09-04

Is there a natural number between 0 and 1?

A proof, s'il vous plaît, not your personal opinion. (Assume the Peano Postulates.)

A proof, s'il vous plaît, not your personal opinion. (Assume the Peano Postulates.)

Elementary geometryOpen question

kweqiwaix 2022-08-31

The necessary and sufficient condition for a non - empty subset W of a vector space V(F) to be a subspace of V is

a,b in F and $\alpha $, $\beta $ in W implies a$\alpha $ + b$\beta $ in W

I need to prove the postulates of vector space with this condition. Hints ?

a,b in F and $\alpha $, $\beta $ in W implies a$\alpha $ + b$\beta $ in W

I need to prove the postulates of vector space with this condition. Hints ?

Elementary geometryOpen question

onetreehillyg 2022-08-19

My graph theory book postulates the if a simple graph with n vertices has at least C(n - 1, 2) + 2 edges then the graph must be Hamiltonian.

This is probably true but I am confused by the notation of what C(n - 1, 2) means?

C usually represents a cycle but clearly not in this case. And whatever function they are referencing takes 2 parameters which is quite strange.

This is probably true but I am confused by the notation of what C(n - 1, 2) means?

C usually represents a cycle but clearly not in this case. And whatever function they are referencing takes 2 parameters which is quite strange.

Elementary geometryOpen question

vroos5p 2022-08-17

Bertrand's postulate says:

For every $n>1$ there is always at least one prime $p$ such that $n<p<2n$.

Is the following statement:

For every $n>3$ there is always at least one prime $p$ such that ${F}_{n}<p<{F}_{n+1}$ (${F}_{n}$ is $n$-th Fibonacci number).

also valid?

If it is invalid, is there a finite or infinite number of ns such that there is no prime between ${F}_{n}$ and ${F}_{n+1}$?

This question is inspiblack by another question. I feel intuitively that it may be interesting, but don't have enough number theory background to tackle it.

For every $n>1$ there is always at least one prime $p$ such that $n<p<2n$.

Is the following statement:

For every $n>3$ there is always at least one prime $p$ such that ${F}_{n}<p<{F}_{n+1}$ (${F}_{n}$ is $n$-th Fibonacci number).

also valid?

If it is invalid, is there a finite or infinite number of ns such that there is no prime between ${F}_{n}$ and ${F}_{n+1}$?

This question is inspiblack by another question. I feel intuitively that it may be interesting, but don't have enough number theory background to tackle it.

Elementary geometryOpen question

schnelltcr 2022-08-16

Is there a smallest real number $a$ such that there exist a natural number $N$ so that:

$n>N\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}{p}_{n+1}\le a\cdot {p}_{n}$?

I believe it can be proved that $n>7\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}{p}_{n+1}\le \sqrt{2}\cdot {p}_{n}$.

$n>N\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}{p}_{n+1}\le a\cdot {p}_{n}$?

I believe it can be proved that $n>7\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}{p}_{n+1}\le \sqrt{2}\cdot {p}_{n}$.

Elementary geometryOpen question

schnelltcr 2022-08-16

Two questions came to mind when I was reading the proof for Bertrand's Postulate (there's always a prime between $n$ and $2n$):

(1) Can we change the proof somehow to show that: $\mathrm{\forall}x>{x}_{0}$, there exists a prime $p$$\in [x,ax]$, for some $a\in (1,2)$?

(2) Suppose the (1) is true, what is the smallest value of ${x}_{0}$?

I'm not sure how to prove either of them, any input would be greatly appreciated! And correct me if any of the above statement is wrong. Thank you!

(1) Can we change the proof somehow to show that: $\mathrm{\forall}x>{x}_{0}$, there exists a prime $p$$\in [x,ax]$, for some $a\in (1,2)$?

(2) Suppose the (1) is true, what is the smallest value of ${x}_{0}$?

I'm not sure how to prove either of them, any input would be greatly appreciated! And correct me if any of the above statement is wrong. Thank you!

Elementary geometryAnswered question

balafiavatv 2022-08-12

Show that the proposition P:

There exists a pair of straight lines that are at constant distance from each other.

is equivalent to the Parallel Postulate Q :

If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

I tried to prove $Q\to P$ then $\mathrm{\neg}Q\to \mathrm{\neg}P$. But for the second part, I can do nothing because as soon as the postulate is supposed to be untrue, the equivalent relation between angles no more exist, therefore it's hard to get congruent triangles as I used to do.

There exists a pair of straight lines that are at constant distance from each other.

is equivalent to the Parallel Postulate Q :

If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

I tried to prove $Q\to P$ then $\mathrm{\neg}Q\to \mathrm{\neg}P$. But for the second part, I can do nothing because as soon as the postulate is supposed to be untrue, the equivalent relation between angles no more exist, therefore it's hard to get congruent triangles as I used to do.

Learning the basic postulates of Geometry is something that you will have to return to, especially if you’re dealing with design and engineering disciplines. Since most of these questions are learned at school, it is helpful when you are looking through the equations, graphs, coordination systems, and more. If you need a more complex postulates geometry explanation, you have to proceed with the simple answers first and then choose something more specific. It’s the safest way to learn more complex things when you know the main postulates first. Start with the equations, look at the graphs, and you’ll get it.