Recent questions in Elementary geometry

Euclidean Geometry
Answered

Davian Lawson
2022-05-02

Midpoint Formula
Answered

Bruce Rosario
2022-04-30

$h:r\mapsto {R}_{r}({P}_{0})=ri\overline{r}$

where r is a unit quaternion and ${P}_{0}=(1,0,0)$ is a fixed point. If a point $r\in {S}^{3}$ is sent by the Hopf map to the point $P\in {S}^{2}$ , a formula can be derived for a particular representation for the cosets. In my case, I want to derive a formula for the ${180}^{\circ}$ rotations around an axes through i and other points in ${S}^{3}$ .

Postulates
Answered

windpipe33u
2022-04-30

The Poisson postulates are:

1. $P(n=1,h)=\lambda h+o(h)$

2. $\sum _{i=2}^{\mathrm{\infty}}P(n=i,h)=o(h)$

3. Events in nonoverlapping intervals are independent

What ensures that $\lambda h\in [0,1]$ irrespective of the value of $\lambda $ ?

Properties of parallelograms
Answered

albusgks
2022-04-30

The figure shows a line L horizontally through the sides of the parallelogram.

This creates two trapezoids and I can intuitively show that if the bases of the trapezoids are not congruent then the areas can not be equal.

I just can not currently see how to relate the intersection with the diagonals.

Any help will be appreciated.

Properties of parallelograms
Answered

vacinammo288
2022-04-30

I know that $det({v}_{1},\dots ,{v}_{n})$ is the oriented volume of the simplex determined by the origin and the vectors ${v}_{1},\dots ,{v}_{n}$ (up to a constant factor depending on the dimension $n$).

But I fell into utter confusion when I tried to make up why, especially when I tried to prove that this formula works for a shifted simplex, too.

What I'm sure is that det is an alternating bi-linear form that fits naturally with an oriented volume function.

What I've found on the net is dependent on what definition is used, and prone to circular reasoning.

Explicit question: how and why is the oriented volume of a simplex related to the determinant of its vectors?

What I've tried: proved it for $n=1,n=2,n=3$, and I've seen that this is not the way to go.

Midpoint Formula
Answered

Oberhangaps5z
2022-04-07

Midpoint Formula
Answered

Ashley Fritz
2022-04-07

a. Find the complex number ${z}_{G}$ that represents the point G

b. Show that $(CG)=\frac{2}{3}(CF)$ and that F is the midpoint of the segment (AB)

Angle Bisectors
Answered

vilitatelp014
2022-04-07

From the similarity, we have $\frac{AL}{{A}_{1}{L}_{1}}}={\displaystyle \frac{CL}{{C}_{1}{L}_{1}}}={\displaystyle \frac{AC}{{A}_{1}{C}_{1}}$. The only way I see from here is to show that $\mathrm{\u25b3}LBC\sim \mathrm{\u25b3}{L}_{1}{B}_{1}{C}_{1}$. Is this necessary for the solution?

Properties of parallelograms
Answered

Bernard Mora
2022-04-07

2) I know that all normed space is a metric space with the metric induced by the norm. Is the reciprocal true ? I mean, is all metric space also a normed space ?

Midpoint Formula
Answered

Elle Weber
2022-04-07

Midpoint Formula
Answered

indimiamimactjcf
2022-04-07

Midpoint Formula
Answered

velinariojepvg
2022-04-06

I know that I have to use the formula for the length of a line and midpoint but I am unsure of what the question is asking.

Euclidean Geometry
Answered

Jordon Haley
2022-04-06

Midpoint Formula
Answered

hyprkathknmk
2022-04-06

Angle Bisectors
Answered

dumnealorjavgj
2022-04-06

$\frac{2\sqrt{bcs(s-a)}}{b+c}$

I have tried using the sine and cosine rule but have largely failed. A few times I have found a way but they are way too messy to work with.

Secondary
Answered

Emily-Jane Bray
2021-04-25

A log 10 m long is cut at 1 meter intervals and itscross-sectional areas A (at a distance x from theend of the log) are listed in the table. Use the Midpoint Rule withn $=5$ to estimate the volume of the log. (in $m}^{3$ )

Show transcribed image text A log 10 m long is cut at 1 meter intervals and itscross-sectional areas A (at a distance x from theend of the log) are listed in the table. Use the Midpoint Rule withn $=5$ to estimate the volume of the log. (in $m}^{3$)

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