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· @tradersharpe · (edited)
$22.13
Integral of 1/√e^2x+1 (Trigo Approach)
![integrateSqrtE2xp -- 00.png](https://steemitimages.com/DQmTumJ59HkqQGJ5HidWz2NyFtnGJUQAvykeefZm8yrBpuZ/integrateSqrtE2xp%20--%2000.png)

-----

I happened to spot [@masterwu's article](https://steemit.com/steemiteducation/@masterwu/integral-of-1-e-2x-1) on the above integral and decided, just for fun, to try doing it via another approach.  As he noted, there is another substitution via hyperbolic functions.  However, this requires more knowledge that is not so-well known to most students.  There is a third type of substitution, that of using a trignometric function which I will demonstrate in this article.

-----

**How to do the Trigonometric Substitution**

The substitution exploits the trigonometric identity ![](https://chart.googleapis.com/chart?cht=tx&chl={\tan^{2}\theta%2b1=\sec^{2}\theta}).  Because ![](https://chart.googleapis.com/chart?cht=tx&chl={e^{2x}%2b1}) _looks like_ ![](https://chart.googleapis.com/chart?cht=tx&chl={\tan^{2}\theta%2b1}), I let ![](https://chart.googleapis.com/chart?cht=tx&ch
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· @mdamanulla69 ·
$0.00
Math
8÷4(3-1) =?
👍  
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· @brogx ·
$0.00
Kids who Count with finger have better chances in math !!
https://ak6.picdn.net/shutterstock/videos/18491926/thumb/1.jpg?i10c=img.resize


Aren't fingers useful? You can point with them, manipulate objects with them, and even create language with them. (Don't even get us started on opposable thumbs.) We may be able to add another finger perk to the roster: According to research, allowing kids to count with their fingers is critical to their overall understanding of math. 

Despite the fact that using your fingers to count has historically been regarded as "not something the smart kids do" in classroom settings, recent neuroscience suggests otherwise. There is a specific region of the brain dedicated to finger perception and representation called the somatosensory finger area. A 2015 study published in Frontiers in Psychology showed that this area lights up when you're solving complex math problems—even when you aren't actually using your fingers to count. Essentially, we "see" a representation of our fingers in our brains when we're crunching numbers. The mathemat
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· @timspeer ·
$27.55
Mathematical Induction
<center>![Logo.png](https://steemitimages.com/DQmfBdzRxU4am56bq2E9gfNSRGXM3qzJAnVda4q5qTpSv53/Logo.png)</center>

<hr></hr>

Mathematical induction is a basic technique used in mathematics to prove a statement holds for some set of numbers. Usually induction is applied to prove a statement that holds for the set of natural numbers and we will demonstrate some examples of how to do this in the current post. 

The idea of induction is fairly simple and is one of the first tools that a mathematician will develop in their bag of mathematical techniques. We start with a given proposition which we will denote by P(n) where the n is meant to signify that our proposition is stated in terms of the natural number n. We would like to prove that the statement P(n) holds for every natural number. Since there are an infinite number of natural numbers we are technically proving an infinite number of propositions. However, induction allows us to do this easily in only a finite number of steps. 

Mathematical induction procee
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· @analealsuarez · (edited)
$0.01
How to obtain the equation of a line knowing its graph
As you can see, the following graph corresponds to a straight line, the objective is to obtain the equation.![gráfica de y=3x+5.png](https://steemitimages.com/DQmTMZVPJ6DWkn8d1E92yXaADyCixsx3c1133MDXuGxe7bz/gr%C3%A1fica%20de%20y%3D3x%2B5.png)
Note that the line intersects with the y-axis at b = 5, this means that the point (0.5) is on the graph of the equation.
Also we have additional information, if we remember the slope of the point of equations of the line y = mx + b, where b is the intersection of the line with the y-axis, so from the graph it follows that b = 5.
Note also in the graph, another point through which the line passes, that is (-5, -10).












![Definitiva y=3x+5.png](https://steemitimages.com/DQmNUtG9Hd1taZd2Wu4GeYfrxqtr915daiCcmaTd8uqPtgB/Definitiva%20y%3D3x%2B5.png)

With this information, we can find the slope of our line:
The slope formula is:
![Pendiente.png](https://steemitimages.com/DQmaGUaACBsHtwCs7go99S1sGTdYxUXkVKCLRnFBLYeT9KQ/Pendiente.png)

Corresponds to points (0.5) and (
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· @sajibbose ·
$0.02
The Reality And Non-Reality Of Mathematics
There's little doubt that mathematics rules the reality roost when it comes to the laws, principles and relationships within the sciences in general and the physical sciences in particular. Further, mathematics plays a dominant role when it comes to the purely economic aspects of our lives and where would sports be without statistics? However, when it comes down to brass tacks, how much of really real reality is actually reflected in our mathematics?

The Reality of Mathematics.

Mathematics is just a shorthand mental concept that simulates reality, or approximates reality or a possible reality or even an imaginary / impossible 'reality'. Mathematics is NOT reality itself. You can mathematically manipulate the alleged extra dimensions in String Theory but that doesn't mean of necessity that these extra dimensions actually exist.
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· @leedslemon ·
$19.27
[Answer by Excel] Mathematics × Programming Competition #8 [答案(使用excel)] 數學 × 程式編寫比賽 (第八回)
<html>
<h2>這次參加了由 @kenchung 舉辦的「數學 × 程式編寫比賽 (第八回)」,有想過用不同的方法去做,最後選了簡單易明的Excel來處理這道題。 帖文在此:https://steemit.com/contest/@kenchung/question-mathematics-programming-competition-8<br>
</h2>
<h2>Thank you @kenchung for hosting Mathematics × Programming Competition #8, I've try to solve the question by some simple excel function. English version below Chinese one, thanks.</h2>
<p>https://steemitimages.com/DQmb33Qwu5vome8xQ2ZLcqFxZmFwV255hPGovzavXSUDtaX/math%26progLOGO-01-01.png<br>
<hr>
</p>
<h2>中文版</h2>
<p>建議和<a href="https://docs.google.com/spreadsheets/d/1lLgwkEZp5gY9E1BX93rdR8kDPomu-AJZFbn5X9Auh58/edit?usp=sharing">解題Excel</a>一起觀看,比較容易理解<br>
這道題主要有幾個方向需要處理:<br>
1.到底數字能不能反轉?<br>
2.如果4位數字能反轉,轉出來的是什麼數字?<br>
3.反轉後的數字有兩個結果<br>
&nbsp;&nbsp;&nbsp;i. 反轉後是相同
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vote your-acct "leedslemon" "answer-by-excel-mathematics-programming-competition-8-excel" 100 true
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· @teukumukhlis ·
$21.33
Thales, Theorem, and Geometry
***
#### <center>*If AC is a diameter, then the angle at B is a right angle (Thales)*</center>

***
<div class="pull-left"><img src="https://upload.wikimedia.org/wikipedia/commons/5/54/Thales_thumb.png" /><center><sub>Credit: Wikimedia Common</sub></center>
</div>

I met Thales in a coffee shop. He was busy scribbling on paper. I went to him. He was surprised to see me. Without being invited to sit down, I had first sat down in a chair. We were facing each other.

I ordered coffee. Thales did not respond to my presence, as if I was not in front of him. Whereas he had been surprised to see me. I realized that I was a troublemaker in their community.

I caught a glimpse of the scrawled paper. I saw a few triangles and numbers and letters. I've heard of the theorem he once brought before the scientists.

"Geometry that will change the future!" I tried to get his attention. Apparently he turned towards me. I smiled triumphantly.

"What do you know about geometry?" Thales asked.

Geometry is a branch of mathematic
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vote your-acct "teukumukhlis" "thales-theorem-and-geometry" 100 true
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· @analealsuarez ·
$1.45
Find the equation of a line knowing its intersection with the axis of the ordinates and its slope.
To explain the procedure of finding the equation of a line that knows the intersection with the axis of the ordinates and the slope, I will use the following problem of linear depreciation:

John bought a new car for $ 10,000. What is the V value of the car after t years, assuming it depreciates linearly each year at a rate of 12% of its original cost? What is the value of the car after 5 years?
# Solution:
We have two variables, are y = V (price of the car), which depends on the variable t which corresponds to time, so that y = V (t) (V is a function of time).
As a result, the car depreciates linearly at a rate of 12% of its initial cost for each year. This means that in 1 year it is depreciated by (12/100) .10000 = 1200, which corresponds to the exchange rate for each year in the cost equation y = V (t).
This rate of change is the slope of the line representing the linear model y = V (t), but as we are dealing with a depreciation model, this slope must carry a negative sign, ie -1200.
This is m = -1200, we 
👍  ,
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vote your-acct "analealsuarez" "6rnkv4-find-the-equation-of-a-line-knowing-its-intersection-with-the-axis-of-the-ordinates-and-its-slope" 100 true
post_comment your-acct "re-analealsuarez-6rnkv4-find-the-equation-of-a-line-knowing-its-intersection-with-the-axis-of-the-ordinates-and-its-slope-20171023t022502793z" "analealsuarez" "6rnkv4-find-the-equation-of-a-line-knowing-its-intersection-with-the-axis-of-the-ordinates-and-its-slope" "" "your reply.." "{}" true

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· @timspeer · (edited)
$21.38
Euclid's Parallel Postulate
<center>![Scaled.png](https://steemitimages.com/DQmWpcVa9W7pCXDCBpi6mhjp7V51ToXURD2NDwfEk8vffq3/Scaled.png)</center>

<hr></hr>

Around 300 BC the mathematician Euclid wrote his mathematical books known today as the <i>Elements</i>. The books remain some of the most widely read books in the world today besides religious texts. In these books Euclid presented his axioms and postulates for what is now called Euclidean geometry. From these axioms he was able to derive new propositions. In this post I want to talk about Euclid's 5th postulate which is also sometimes called the Parallel Postulate. 

In any system of mathematics there is a need for axioms or postulates. These axioms are statements that are assumed to be true or are assumed to be intuitively obvious without proof. Without the axioms mathematicians would have no foundation from which to start working. From the axioms mathematicians then go on the develop more elaborate theories and propositions which might be far from obvious but which can be proven 
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vote your-acct "timspeer" "euclid-s-parallel-postulate" 100 true
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· @tradersharpe · (edited)
$19.26
Simplifying Roots
![square_root00_b.png](https://steemitimages.com/DQmWUSMiteZ2qnQmFbw7WC96oYiSNnvjdVzBfWdWoDQgSvJ/square_root00_b.png)

-----


Just like Facebook relationships, roots can get "complicated".  No, I am not talking about roots of plants or trees.  I am talking about things like ![](https://chart.googleapis.com/chart?cht=tx&chl={\sqrt{48}}), ![](https://chart.googleapis.com/chart?cht=tx&chl={\frac{15}{\sqrt{3}}}), ![](https://chart.googleapis.com/chart?cht=tx&chl={\frac{6}{\sqrt{20}}}) and ![](https://chart.googleapis.com/chart?cht=tx&chl={\sqrt[3]{54}}).  These are expressions involving square roots or cube roots.  There can be other types of roots as well.

Such expressions are called "[surds](https://en.wikipedia.org/wiki/Nth_root)".  If you think they are absurd, you are right!  That is because most of these expressions are [irrational numbers](https://en.wikipedia.org/wiki/Irrational_number). Unless the root involved is also a whole number, the decimal expansion of the root would go on forever without any re
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vote your-acct "tradersharpe" "simplifying-roots" 100 true
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· @timspeer · (edited)
$6.26
What is a Torus?
<center>![Logo.png](https://steemitimages.com/DQmchqxk4Fq1BcmSfRSyU3Ww24MRs1CTfU6XYwwbFgm9DDr/Logo.png)</center>

<hr></hr>

In my last post on topological objects we saw how to construct a Möbius strip by gluing together two edges of a rectangle with a half twist. In this post I will show you how to construct a torus using a similar type of construction. A torus is often described as a shape which looks like a donut.

To create a torus we will start with a square with arrows on the edges as follows:

<center>![1.png](https://steemitimages.com/DQmZVaMWsnqKjaacRbKsqoNGur36o2tLykrSqr21djUzif2/1.png)</center>

Recall that the arrows tell us which sides to glue together and which orientation to do it with. In the picture above the arrows show that we should identify the left and right edges of the square and the top and bottom edges of the square while preserving the direction of the arrows. 

Let us do this one step at a time. Note that it does not matter the order in which we do this, we will get a torus eithe
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vote your-acct "timspeer" "what-is-a-torus" 100 true
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· @steemitlovers · (edited)
$2.91
Math lessons are easy to learn and fun
Hi, Everyone....

Mathematics is considered a very boring lesson by some students who do not understand and understand how to learn math. Students assume that math lessons are very scary. Playing with numbers makes students feel confused and dizzy when learning math. Actually, they do not yet know how to successfully learn mathematics, whereas math becomes a very fun lesson if you master the key of learning math.
<center>http://lonesomebird.com/wp-content/uploads/2017/01/i-am-a-student-1412778_640.jpg
<sup> [Image source](http://lonesomebird.com/wp-content/uploads/2017/01/i-am-a-student-1412778_640.jpg)</sup></center>
The main key in learning mathematics is a strong adherence by having a curiosity about counting operations in learning math. In addition to sticky, intentions are also very important in doing something, especially in terms of learning math.

The sum of (+), the difference (-), Multiplication (x), and Division (/) are the roots of the mathematics lesson that you must learn. All the students who r
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· @analealsuarez · (edited)
$0.00
Familia de parábolas
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![familia de parábolas5.png](https://steemitimages.com/DQmeMJGuXC9C51YeapWJRy8MGXwzVLpM5BQ7t5AwFWmmKHq/familia%20de%20par%C3%A1bolas5.png)






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vote your-acct "analealsuarez" "familia-de-parabolas" 100 true
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· @sayee · (edited)
$0.37
Poems for kids
<html>
<p><strong>The Rabbit</strong></p>
<p><strong>The rabbit had stored 16 carrots</strong></p>
<p><strong>Divided into groups of four</strong></p>
<p><strong>The rabbit gave each of his four babies a batch</strong></p>
<p><strong>How many did each one get?</strong></p>
<p><strong>This short poetic riddle can be given to the kids to help them learn math quickly.</strong></p>
<p><img src="https://cdn.pbrd.co/images/GPXI61G.png" width="758" height="720"/></p>
<p><strong>h</strong></p>
<p><br></p>
<p><strong>The secret word</strong></p>
<p><strong>I am a support for those who cannot walk alone</strong></p>
<p><strong>I protect you from showers&nbsp;</strong></p>
<p><strong>I can be folded or sometimes stand straight and tall</strong></p>
<p><strong>I have been useful to all&nbsp;</strong></p>
<p><strong>Answer : umbrella</strong></p>
<p><img src="https://cdn.pbrd.co/images/GPXL6sW.png" width="280" height="340"/></p>
<p><br></p>
<p><strong>Such riddles can be made to make study time more fun.</strong></p>
<p><
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vote your-acct "sayee" "poems-for-kids" 100 true
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· @firstamendment · (edited)
$0.11
Mathematics × Programming Competition #8 - Programmatic solution in java
This is a solution to @kenchung math and programming challenge:
https://steemit.com/contest/@kenchung/question-mathematics-programming-competition-8#

which basically asks if make numbers in a digital clock type format (or standard 4 function calc) on a card, what is the least amount of cards needed-assuming you can turn the cards upside down-and not worry if the one is aligned left or right-up to the number 9999. Read the link to get a visual.

This is a very simple program.  

Because we include "0000" or just "0", we have a total of 10000 numbers total.
  And so I created a binary array of 10k binary objects.  i just called the array data.  I would ensure that all the values are set to false by running a for loop at the start of the main routine.  
  because it asks us a quantity, I needed to create a variable to count each unique solution and of course set it to zero.  

  I proceeded to create 4 for loops each creating a number between 0-9.  This produces 4 digits.  
I put the 4 digits together in a subr
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vote your-acct "firstamendment" "mathematics-programming-competition-8-programmatic-solution-in-java" 100 true
post_comment your-acct "re-firstamendment-mathematics-programming-competition-8-programmatic-solution-in-java-20171023t022502823z" "firstamendment" "mathematics-programming-competition-8-programmatic-solution-in-java" "" "your reply.." "{}" true

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· @vincentyip ·
$9.15
數學 × 程式編寫比賽 (第八回) -- 我的解法
這次我又參加了 @kenchung 的「數學 × 程式編寫比賽 (第八回)」了,真的非常益智和有趣!


帖文可到這裡看一看:https://steemit.com/contest/@kenchung/question-mathematics-programming-competition-8

https://steemitimages.com/0x0/https://steemitimages.com/DQmb33Qwu5vome8xQ2ZLcqFxZmFwV255hPGovzavXSUDtaX/math%26progLOGO-01-01.png

要解決這條問題,我們首先要思考有那些數字在旋轉後會成為一個有意義的數字。我們可以由0-9999之中逐個數字檢查,嘗試將那數字旋轉,如果旋轉後是另一個有意義而且比自己大的數字,便在那個數字作標記。

所以檢查完成後,沒有標記的數字的數量便是我們的答案了!


程式如下:


```

var alts=[0,1,5,-1,-1,2,9,-1,8,6];

var log=[];
var x=0;

for(var i=0; i<10000; i++)
    log[i]=false;

for(var i=0; i<10000; i++){

	if(log[i]) continue;
	log[i]=true;
	x++;

    var b=i.toString();

    if(i<1000) b='0'+b;
    if(i<100) b='0'+b;
    if(i<10) b='0'+b;
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vote your-acct "vincentyip" "676hxw" 100 true
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· @berjis ·
$15.56
Amazing Number Pyramids
The following equalities are obvious, but they are beautiful nonetheless.

````
        1 × 1          =         1
       11 × 11         =        121
      111 × 111        =       12321
     1111 × 1111       =      1234321
    11111 × 11111      =     123454321
   111111 × 111111     =    12345654321
  1111111 × 1111111    =   1234567654321
 11111111 × 11111111   =  123456787654321
111111111 × 111111111  = 12345678987654321


       1 × 9 + 2 = 11
      12 × 9 + 3 = 111
     123 × 9 + 4 = 1111
    1234 × 9 + 5 = 11111
   12345 × 9 + 6 = 111111
  123456 × 9 + 7 = 1111111
 1234567 × 9 + 8 = 11111111
12345678 × 9 + 9 = 111111111


              12 - 1 = 11
            123 - 12 = 111
          1234 - 123 = 1111
        12345 - 1234 = 11111
      123456 - 12345 = 111111
    1234567 - 123456 = 1111111
  12345678 - 1234567 = 11111111
123456789 - 12345678 = 111111111
````

I hope you enjoyed these beautiful equations. Another type of beautiful formulas are continuous fractions and infinite sum ser
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vote your-acct "berjis" "amazing-number-pyramids" 100 true
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· @dkmathstats ·
$19.39
Money Exercises For Kids With Coins
Hi there. One of the most useful mathematics lessons for young kids is money counting. This post features exercises with Canadian coins in dollars and cents. For those in different regions, you may substitute the Canadian currency with your local currency.

Note: The one cent penny is no longer used in Canada. Prices are rounded to the nearest five cents.

<center><img src="http://www.kiplinger.com/slideshow/saving/T065-S002-rules-for-raising-money-smart-kids/images/stock-boy.jpg" /></center>
<center><a href="http://www.kiplinger.com/slideshow/saving/T065-S002-rules-for-raising-money-smart-kids/images/stock-boy.jpg">Featured Image Source</a></center>


#### Coins & Their Denominations
---

Each coin has their size and their own monetary value. Let's take a look at the Canadian coins and their value.

Coin Name | Amount
------------ | -------------
Penny | 1 cent = $0.01
Nickel | 5 cents = $0.05
Dime | 10 cents = $0.10
Quarter | 25 cents = $0.25
Loonie | 100 cents = 1 dollar = $1.00
Toonie | 200 cents = 2 doll
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· @braincoach ·
Math Can Be A Problem Without A Foundation
![](https://steemitimages.com/DQmQFdUokWxbKQKLmDDVqcEuW6BzZwzagMcV6xkbLXzoKNX/image.png)How  many children do you know struggle with math?  You may be surprised to know there are gifted children who have difficulty, as well.  The foundation upon a child's early development is formed  or the lack thereof can cause difficulty at any age if the brain organization and processing abilities are not developed enough to serve for a basis to even learn ones math facts successfully. 

Dr. Jan Bedell guides parents through this maze of necessity and illuminates how a parent can go about lighting the way toward successful mastery of math, math concepts, receiving, storing, and recalling all that goes along with this vital skill we utilize in all areas of our lives.  

She will cover many foundational practices such as:

 

1. Rote counting – Counting CD
2. Understanding quantity – first count accurately, then be able to look at fingers, pictures on a page, and dice and be able to recognize the quantity
 

3. Counting
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