IES Math Club

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“May Allah protect our Brothers & Sisters in Palestine”

For an example....
If I asked you to add all the numbers between one and one hundred, you will stay for hours adding every number with the others, but if you added 1 and 100 this will add up to 101, and if you add 2 and 99 it will also add to 101, 3 and 98 are the same.
So you’ll add 101 for 49 times and the last remaining time will be 50+51 and there will not be a middle number because the number of terms you want to add is an even number, so that will make it 101 for 50 times.
So instead of adding all the numbers between 1 and 100 you’ll just multiply 101 by 50 and the answer will be 5050.
(As in example 1)
But what if it’s an odd number? Like adding all the numbers from zero to one hundred
that will make the algorithm different because you will add an odd number of terms which is
101 terms
If you tried to make the same algorithm of adding the first and the last terms together, you
will add 0+100 and that will add up to 100, 1+99 and that will also add up to 100 , 2+98 and
so on...but there will be a middle number this time and that is 50, so you will add 100 for
fifty times and there will be the number 50 with no opposite term to add... so you will add it
after you finish your multiplication (as in example 2)
The summation has so many uses such as:
• Some calculations that are made by statisticians
• Calculating Euler’s number
• Used in the binomial theorem for integer positive power

Uses of factorial:
- Permutations and Combination
- Probability
- Series Expansion
- Binomial Theorem
- Hypergeometric Functions
- Gamma Function
- Combinatorial Optimization problems, such as the traveling salesman problem
and the knapsack problem.
- Computer Science

Who is Euler?
Leonhard Euler was a Swiss mathematician who made enormous contributions to a wide range of mathematics and physics including analytic geometry, trigonometry, geometry, calculus and number theory

What is Euler’s number?
It’s an irrational number represented by the letter e, Euler's number is 2.71828..., where the digits go on forever in a series that never ends or repeats (similar to pi). Euler's number is used in everything from explaining exponential growth to radioactive decay

Some uses of Euler’s number:
Euler's number frequently appears in problems related to growth or decay, where the rate of change is determined by the present value of the number being measured. One example is in biology, where bacterial populations are expected to double at reliable intervals. Another case is radiometric dating, where the number of radioactive atoms is expected to decline over the fixed half-life of the element being measured.

How Is Euler's Number Used in Finance?
Euler's number appears in problems related to compound interest. Whenever an investment offers a fixed interest rate over a period of time, the future value of that investment can easily be calculated in terms of e.

As Archimedes said:
if you put a circle between two hexagons; then, the perimeter of the circle is between the area of the two hexagons; and if you increase the number of the sides of the polygons, you get a closer ratio to π. (As shown in image no. 3 )
Pi (π) has been known for almost 4000 years, but even with all that time, we still can't calculate its actual value. The Babylonians calculated pi to be 3, and an ancient tablet indicated 3.125 as a closer approximation. The Egyptians calculated pi to be around 3.1605. Archimedes approximated pi by using the Pythagorean Theorem to find the areas of two regular polygons inscribed within and circumscribed around the circle. Zu Chongzhi, a Chinese mathematician and astronomer, calculated pi to be 355/113 by starting with an inscribed regular 24,576-gon and carrying out lengthy calculations involving hundreds of square roots. The symbol for pi was introduced by William Jones in 1706 and popularized by Leonhard Euler in 1737.

Pi has numerous practical applications, including solving geometry problems like finding the area of a circle and electrical applications. Statisticians use pi to track population dynamics, and medicine benefits from pi when studying the structure of the eye. Biochemists use pi to understand DNA's structure and function, and physicists use it in their calculations when looking into the behavior of fluid ripples. Clock and aircraft designers use pi to design pendulums and calculate areas of the aircraft's skin, respectively. Navigation, such as GPS, and measuring the magnetic permeability of a body also use pi. In short, pi is a fundamental mathematical constant with an extensive range of uses in various fields of study.

It is the inverse function of the Exponential function
1. Equations involving exponentials may be solved fast and simply using logarithms.
2. Logarithms make it easier to multiply and divide very big numbers.
3. Applications of logarithms in science include determining concentrations or dilutions, calculating pH, and working with sound waves and acoustic measurements.
4. Changes over time are frequently measured using logarithmic scales, such as earthquakes on the Richter scale or decibels for sound intensity levels.
5. Logarithms may also be applied in statistics to approximate probabilities, estimate population sizes from sample sizes, and other tasks.

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ال pythagorean theorem إلي كلنا اتعلمناها في المدرسة ليها استخدامات كتيرة جدا في حياتنا اليومية

زي ال الهندسة المعمارية و البناء🦺🧱
التعرف على الوجوه بكاميرات المراقبة 📸
التنقل و السفر عن طريق البحر علشان نلاقي أقصر مسافة ممكنة لوجهتنا 🛳️ ،

و غير كده كتير........

The Pythagorean theorem that all of us had to learn about at school has numerous uses in our daily life

such as: Engineering and Construction fields 🦺🧱 (obviously)
Face recognition in security cameras 📸 Navigation and traveling in the sea to find the shortest distance 🛳️

and so on......

How to solve a cubic equation

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Did you know that the cubic equation we are using now was a secret one day?
In the 16th century, the Italian mathematician Scipione del Ferro was able to find a solution for the cubic equation (x + ax =b). But Del Ferro didn’t tell anyone about the solution, until Del Ferro was about to die. In that time, he said the solution for his student “Antonio Fior”.
But as his teacher, Antonio didn’t tell anyone about the solution to be the cleverest among the people.
As in the past they were doing “Math dules” something like competitions in math dedicated for equations. So, every time someone goes to Fior to challenge him, nothing happens except Fior defeating him.
The situation was like this until Niccolo Fonta Tartaglia challenged Fior. Tartaglia was able to guess the types of equations which Fior was solving, but he still doesn’t know how to solve these equations.
So Tartaglia sent some equations to Fior and Tartaglia was sure that Fior will be unable to solve them. Then Fior sent Tartaglia another equation. Tartaglia has been solving these equations in about 40 days until he found solution more effective than Fior’s solutions. But on the other hand, Fior was unable to solve any of the equations Tartaglia sent to him.
In that time Tartaglia was very famous because he was the only one who defeated Fior. But as usual he didn’t say how to solve the equation. Tartaglia was therefore not willing to reveal the solution process he had used to answer Fior’s questions for fear that Messer Zuanne would infer from it the solution formula for the cubic equations of the form x3 + bx = c, which for the moment Niccolo had no intention to give away. In those days it was the custom among mathematicians to refrain from announcing their results; keeping them secret could help attract students as well as serve as a weapon in public contests. Tartaglia followed the custom, as obviously did the “great mathematician” mentioned by Fior "Scipione del Ferro. He was getting famous more and more and the mathematicians in Italy was sending to him to know the solution but he always refuses to say the answer.
until someone called “Gerolamo Cardano” was usually sending and begging Tartaglia to know the solution but as usual Tartaglia refused but Cardano decided to do like what Tartaglia did with Fior by sending to him some equations but Tartaglia refused.
Cardano didn’t give up and was begging Tartaglia more and more until Tartaglia said yes. But Tartaglia wrote an indent to be sure that the solution will be a secret between them, and Cardano agreed.
After that he was thinking how did Tartaglia reached this solution. Until one day he was able to develop it and made a comprehensive solution. But in Cardano’s solution he used Tartaglia’s solution so, he was unable to publish his solution because of that indent.
This was only until 1543, when Cardano travelled to Bologna city in Italy which contains the original books which belongs to Scipione Del Ferro. And then Cardano found out the Del Ferro was the first one to find the solution.
Then he concluded that the Indent between him and Tartaglia isn’t something. So, after that Cardano was able to share his solution with all the people when he published his book “The great art or the rules of Algebra” and in that book he told the untold truth about the solution of the cubic equation from the very beginning.
هل في يوم من الأيام كنت تعرف ان حل المعادلة التكعيبة اللي بنستخدمها دلوقتي كانت سر في يوم من الأيام؟
في القرن ال 16، عالم الرياضيات الإيطالي شبوني ديل فيرو قدر يحل المعادلة التكعيبية. بس ديل فيرو كان مش عايز يقول لحد على حله، لغايت لما ديل فيرو كان على وشك الموت. ساعتها قرر انه يقول الحل ل الطالب بتاعه "أنطونيو فوار".
بس زي استاذه، أنطونيو مرضاش يقول لحد على حل المعادلة عشان يفضل أذكى واشطر حد بين الناس.
زمان كانوا بيعملوا تحديات في الرياضيات حاجة كده زي منافسة بس مخصصة اكتر لحل المعادلات. ف كان كل مرة واحد يروح ل فيور عشان يتحداه مفيش أي حاجة بتحصل غير ان فيور بيهزم الشخص ده.
الوضع فضل كده لغايت لما نيكولا فونتا تار تاليا اتحدي فيور. تارتاليا قدر يحدد نوع المسائل اللي فيور بيحلها، بس بردوا مقدرش يعرف هو بيحلها ازاي.
ف تارتاليا بعت شوية مسائل ل فيور وتارتاليا كان متأكد ان فيور مش هيعرف يحل المسائل دي. بعد كده فيور بعت مسائل ل تارتاليا.
تارتاليا فضل حوالي 40 يوم بيحل في المسائل دي لغايت لما وصل ل حل أكثر كفاءة من حل فيور. لكن فيور مقدرش يحل أي مسألة من المسائل اللي تارتاليا بعتهاله.
في الوقت ده تارتاليا اتشهر جدا لأنه كان الوحيد اللي قدر يغلب فيور. بس كالعادة مقالش المعادلة بتتحل ازاي. عشان كده تارتاليه مكنش على استعداد انه يكشف عن عملية الحل اللي استخدمها في الإجابة على أسئلة فوار لأنه كان خايف من أن ماسر زوان يستنتج منه صيغة الحل للمعادلة التكعيبية x3 + bx = c ، واللي مكنش عند نيكولو في الوقت الحالي نية التخلي عنها. وكان من المعتاد في الأيام دي بين علماء الرياضيات انهم يمتنعوا عن إعلان نتائجهم ؛ و ده كان بيساعدهم علي جذب الطلاب بالإضافة انهم بيستخدموها كسلاح في المسابقات العامة. و تارتاليه اتبع العادة بتاعة علماء الرياضيات ، زي م عمل "عالم الرياضيات العظيم" اللي ذكره فوار “شبونه ديل فيرو".و شهرته يوم ورا الثاني كانت بتزيد وكان في علماء رياضيات كتير في إيطالية بيبعتوله عشان يعرفوا حل المعادلة بس هو دايما كان بيرفض.
لغايت ما في يوم من الأيام "جيرولامو كاردانو" كان باستمرار بيبعت وبيترجي تارتاليا عشان يعرف الحل بس تارتاليا كان برضه بيرفض. بس كاردانو قرر يعمل نفس اللي عمله تارتاليه مع فيور عن طريق انه يبعتله مسائل يحلها بس تارتاليه رفض.
كاردانو مستسلمش وكان بيترجى تارتاليه اكتر واكتر لغايت لما تارتاليه وافق. بس تارتاليه كنت عقد عشان يأكد على ان الحل هيفضل سر بينهم، وكاردانو وافق.
بعد كده كاردانو كان بيفكر ازاي تارتاليه وصل للحل ده. لغايت لما طور الحل وبقي اشمل. بس كاردانو استخدم في الحل بتاعه الحل بتاع تارتاليه، ف كان مش هيقدر ينشر الحل بتاعه بسبب العقد.
الكلام ده كان لغايت 1543، لما كاردانو سافر ل مدينة بولونيا الإيطالية اللي كان فيها الكتب الأصلية بتاعت ديل فيرو. وبعدها اكتشف كاردانو ان ديل فيرو كان اول شخص يحل المعادلة.
ومن هنا اكتشف ان العقد اللي بينه وبين تارتاليه مالوش لازمة. ف بعدها كاردانو قدر بنشر الحل مع الناس لما نشر الكتاب بتاعه" الفن العظيم او قواعد الجبر" وفي الكتاب ده هو قال الحقيقة اللي محدش يعرفها عن حل المعادلة التكعيبية من الأول جدا.

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We are a society dedicated to educating people about math and its associated fields. It was first founded by a group of students who are passionate about disseminating knowledge about math and related subjects.

Vision
1-we will provide easy useful scientific information about math .

2-We will present diverse fields of math such as Calculus.

Mission
It is our first season, so stay tuned for a lot of information and experiences about mathematics. Our goal is not just to explain, but to make you love mathematics and learn it easily, and there will be many surprises.
Stay tuned.....

احنا طلاب هدفنا أن احنا نحبب الناس في مادة الماث ده غير أن احنا هنساعدهم كمان في المذاكره يعني هيكون في شرح وحل مع بعض مش هنسيبك تايه

1 هنقدم معلومات علمية سهلة ومفيدة فالماث.

2 هنقدم مجالات متنوعة في الماث زي حساب التفاضل والتكامل.

وطبعا احنا معاكم للنهايه .والبوست ده بيعلن عن بداية السيزون الاول انتظرونا قريبا..