The Radon Transform – Life-Saving Mathematics

In 1917, Austrian mathematician Johann Radon discovered a formula that is now called the Radon Transform. It was mostly forgotten and unused until 1970, when it became the key to making CT Scans possible.

The graphic shows how the CT scanner works:

1. A narrow band of X-Rays is sent through a “slice” of the organ to be imaged. The emerging rays are attenuated according to the average density of the tissue that each ray has passed through.

2. After the X-Ray source and detector rotate slightly, a new attenuation curve is recorded.

3. Using a large number of these attenuation curves, each at a different angle, the Radon Transform mathematics allows a computer to calculate the density of each point in the slice.

4. The source and detector then move longitudinally, and image the adjacent slice.

These adjacent slice images give the radiologist a three dimensional view of the organ, instead of the silhouette-like image that a conventional X-Ray produces.

Ironically, Johann Radon died (in 1956) of cancer, and cancer is one of the diseases whose treatment has benefited most from CT scans.

@infinitymath

Epitaph (by Kepler, for himself)
Mensus eram coelos, nunc Terrae metior umbras.
Mens coelestis erat, corporis umbra jacet.

I used to measure the Heavens, now I measure the shadows of Earth.
The mind belonged to Heaven, the body's shadow lies here.
@infinitymath

There is no smallest among the small and no largest among the large,
But always something still smaller and something still larger.

Quoted in E Maor, To Infinity and Beyond: a Cultural History of the Infinite
@infinitymath

@infinitymath
پادکست های "برگ هایی از تاریخ ریاضیات" به کمک دانشجویان ریاضی دانشگاه ملایر و کانال بی نهایت تهیه شده است و هدف این بوده است که ریاضیدانان بزرگ ایرانی و غربی به صورت کوتاه معرفی شوند. منبع اصلی این فایل های صوتی کتابهای "آشنایی با تاریخ ریاضیات" نوشته هاوارد ایوز و "ریاضیدانان نامی" نوشته اریک تمپل بل و همچنین سایت ویکی پدیا بوده است، از دانشجویان ریاضی دانشگاه ملایر که زحمت ضبط فایل ها را قبول کردند تشکر میکنیم. هرگونه پیشنهاد و ایده ای در این مورد دارید از راه های ارتباطی کانال با ما در میان بگذارید.
@h13940620

@infinitymath
برگ هایی از تاریخ ریاضیات، دکتر مریم میرزاخانی، بانوی ریاضیات ایران
این فایل صوتی به کمک آقای قهرمانی، دانشجوی کارشناسی ریاضی، پردیس شهید بهشتی تهران، دانشگاه فرهنگیان و ادمین کانال ریاضیات از نگاهی نو، میکس و صدگذاری شده است. با تشکر فراوان از ایشان.
کانال ریاضیات از نگاهی نو:

🆔 @math_new

🎥 تناقض هتل بی‌نهایت!
بی‌نهایت چیه؟ آیا تا به حال فکر کردین چقدر بزرگه؟
📡 @infinitymath

👆👆👆👆👆👆👆👆👆
Each dot chases the one before it at a constant speed, slower than the one it is chasing by a fixed ratio. As a result each dot converges to a smaller circle inside the one it is chasing. If they had the same speed, they would get closer and closer to catching up, but would take infinitely long to do so.
If they were faster then they would catch up with each other in a finite length of time.
@infinitymath

Visualization from "Distribution of the units digit of primes"

In the animation above, the first frame shows how many of the first 100 primes end in 1, 3, 7 and 9. They all occur roughly the same number of times, so the four squares are almost exactly the same shade of red. The next frame shows how frequently a prime ending in 1 is followed by a prime ending in 3 - and so on.
A structured pattern emerges, with the final frame showing the distribution of final digits in strings of 8 consecutive primes (for the first 2 million primes)
@infinitymath

six conic sections
@infinitymath

Fermat’s Christmas Theorem

In a letter dated December 25, 1640, French mathematician Pierre de Fermat described a remarkable property of prime numbers that he had discovered. Because of the date, it is usually called the Christmas Theorem.

To describe what the theorem says, first note that all prime numbers except 2 are odd numbers. This means that if we divide these primes by 4, the remainder will be either 1 or 3. For example, 13 is a “1 prime” because 13 / 4 leaves a remainder of 1.

In the letter, Fermat claimed that all “1 primes” are equal to the sum of two squares. For example, 13 = 3² + 2². Also, he said, none of the “3 primes” can be written this way. The graphic shows how this works out for a few selected prime numbers.

In the letter, Fermat stated that he had proved his theorem, but did not give the proof. Leonard Euler published a proof 112 years later.
@infinitymath

سلام بر دوستان .

معرفی مقاله :

نام مقاله : "توپولوژی عمومی و پیدایش آن".

نویسنده : پروفسور مهدی بهزاد

نام مجله : یکان

شماره ی هفتم از مجله ی یکان مرداد ماه 1343

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بطور کلی به کمک مجرد کردن یک ایده ی آشنا و معمول ریاضی در یک یا چند جهت ممکن است قضایایی کشف نمود که از نظرهای مختلفی قابل استفاده باشد .... توپولوژی عمومی یکی از شعبه های ریاضی است که کم وبیش بر این اصل توسعه یافته است... گرچه تاریخ توپولوژی خیلی کهن است ولی... بیشتر فضاهای معروف در قرن 19 ظهور کردند ...

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