Recent questions in Elementary geometry

Postulates
Answered

Lucas Roman
2022-06-04

$A\vee \mathrm{\neg}A$

is rejected 'a priori' in the sense that we can only prove the validity of $A$ or $\mathrm{\neg}A$. My question is: given the rejection of these principles, in particular the second, is it still possible to keep the validity of the mathematical analysis within the intuitionism? Or maybe, accepting the intuitionistic approach, you need to develop a new kind of analysis, because, for example, it's impossible to use the 'reductio ad absurdum' to prove a theorem? Thanks

Angle Bisectors
Answered

Cason Leblanc
2022-06-04

Angle Bisectors
Answered

Payton Salazar
2022-06-04

I'm trying to prove that angle bisectors in a triangle intersect at a single point, but I need to show it analytically, i.e using line equations and distance between points. I'm familiar with proofs using geometry and vectors, but couldn't manage to show analytically. I can't use the formula of angle between lines or distance of point from a given line.

Things I've tried:

1. angle bisector theorem.

2. Writing equations of sides as $Ax+By+C=0$ and then creating the equation of angle bisector - quite messy and I believe there is a lot easier way.

Thanks!

Euclidean Geometry
Answered

Estrella Le
2022-06-03

Angle Bisectors
Answered

Marquis Cooper
2022-06-03

I am not sure how to approach the problem. The most "obvious" thing that we can do is to find the hypotenuse $c=\sqrt{{a}^{2}+{b}^{2}}=25$ of the triangle $\mathrm{\u25b3}ABC$. Therefore, ${m}_{c}={\displaystyle \frac{1}{2}}\cdot 25=12.5$. On my sketch $AC=15$and $BC=20$. What to do next?

Angle Bisectors
Answered

amuguescaet3jf
2022-06-03

By the angle bisector theorem we have $\frac{AC}{AE}=\frac{CB}{BE}$ and $\frac{AB}{AF}=\frac{BC}{FC}$. How do I proceed after this? Hints would be appreciated.

Euclidean Geometry
Answered

Kallie Arroyo
2022-06-02

Postulates
Answered

patzeriap0
2022-05-29

Postulates
Answered

Alessandra Clarke
2022-05-29

Bertand's postulate shows us that $4{p}_{n-2}\ge {p}_{n}$ but can we improve on this?

any ideas?

Postulates
Answered

Angel Malone
2022-05-29

The question is

1) Euclids ${4}^{th}$ postulate is "That all right angles are equal to one another". Why is this not obvious?

My answer:

When I read this question I am like it is obvious, so I got kind of confused. But I took a crack at it anyways.

If you read the postulate. This is not obvious because you dont know if the right angle is a right angle. What if a triangle was drawn differently but with one line perpendicular to another. You need to know if the line is perpendicular or not, and that is why it is not obvious.

Could someone tell me if that is right or should I add in more info.

Postulates
Answered

qtbabe9876a9
2022-05-28

Postulate 13: Every non-empty set of real numbers that is bounded above has a least upper bound (sup).

Why is this postulate true? Any proof/intuition behind it?

Edit: Let me pose a few questions.

1. Suppose I decide to devise a pathological function $\mathbb{R}$$\to $$\mathbb{R}$ which is bounded above but has no supremum. Why will I fail to find such $f$? If you simply take it as an axiom, there's no guarantee I won't be successful.

2. Suppose $S$ is an arbitrary non-empty set of real numbers that is bounded above. Does there exist an algorithm to determine $sup(S)$?

Midpoint Formula
Answered

res2bfitjq
2022-05-27

Midpoint Formula
Answered

groupweird40
2022-05-26

Euclidean Geometry
Answered

tuehanhyd8ml
2022-05-15

Properties of parallelograms
Answered

Merati4tmjn
2022-05-15

I find this property very useful while solving different problems on Quadrilaterals & Polygon,so I am very inquisitive about a intuitive proof of this property.

Euclidean Geometry
Answered

Edith Mayer
2022-05-14

Euclidean Geometry
Answered

Waylon Mcbride
2022-05-13

Properties of parallelograms
Answered

Jayden Mckay
2022-05-10

$\vartheta (z+\gamma )={e}^{2i\pi {a}_{\gamma}z+{b}_{\gamma}}\vartheta (z)$

for every $\gamma \in \mathrm{\Gamma}$, and ${a}_{\gamma},{b}_{\gamma}\in \mathbb{C}$.

Exercise: A Theta function never vanishes iff $\vartheta (z)={e}^{p(z)}$ with $p(z)$ a polynomial of degree at most 2.

Hint: The "only if" part is trivial. The hint is: show that $\mathrm{log}(\vartheta (z))=O(1+|z{|}^{2})$. I tried to apply log on both sides, or derive one and two times, or everything I could have thought of. I don't get where the square comes from.

Angle Bisectors
Answered

Jace Wright
2022-05-10

Can anyone suggest how to approach this example?

Euclidean Geometry
Answered

tiyakexdw4
2022-05-10

While elementary geometry is often encountered by college students as they are dealing with the basic design and modeling tasks, it is often necessary to implement equations or turn to Euclidean Geometry to determine the values of shapes and figures that are related to axioms and different theorems. When you are dealing with flat surfaces, it will help you to work with straight line segments. The same relates to those cases when you need to calculate formulas by using midpoint formula example problems that you can find below as you are dealing with the elementary problems in Geometry. If you find it ov