A Pair Of Chapel Ceilings - Both In Wroclaw, Poland

My final grade in number theory should be the score of my last two exams combined. 

Interesting facts about stars

Stars are giant, luminous spheres of plasma. There are billions of them — including our own sun — in the Milky Way Galaxy. And there are billions of galaxies in the universe. So far, we have learned that hundreds also have planets orbiting them.

1. Stars are made of the same stuff

All stars begin from clouds of cold molecular hydrogen that gravitationally collapse. As they cloud collapses, it fragments into many pieces that will go on to form individual stars. The material collects into a ball that continues to collapse under its own gravity until it can ignite nuclear fusion at its core. This initial gas was formed during the Big Bang, and is always about 74% hydrogen and 25% helium. Over time, stars convert some of their hydrogen into helium. That’s why our Sun’s ratio is more like 70% hydrogen and 29% helium. But all stars start out with ¾ hydrogen and ¼ helium, with other trace elements.

2. Most stars are red dwarfs

If you could collect all the stars together and put them in piles, the biggest pile, by far, would be the red dwarfs. These are stars with less than 50% the mass of the Sun. Red dwarfs can even be as small as 7.5% the mass of the Sun. Below that point, the star doesn’t have the gravitational pressure to raise the temperature inside its core to begin nuclear fusion. Those are called brown dwarfs, or failed stars. Red dwarfs burn with less than 1/10,000th the energy of the Sun, and can sip away at their fuel for 10 trillion years before running out of hydrogen.

3. Mass = temperature = color

The color of stars can range from red to white to blue. Red is the coolest color; that’s a star with less than 3,500 Kelvin. Stars like our Sun are yellowish white and average around 6,000 Kelvin. The hottest stars are blue, which corresponds to surface temperatures above 12,000 Kelvin. So the temperature and color of a star are connected. Mass defines the temperature of a star. The more mass you have, the larger the star’s core is going to be, and the more nuclear fusion can be done at its core. This means that more energy reaches the surface of the star and increases its temperature. There’s a tricky exception to this: red giants. A typical red giant star can have the mass of our Sun, and would have been a white star all of its life. But as it nears the end of its life it increases in luminosity by a factor of 1000, and so it seems abnormally bright. But a blue giant star is just big, massive and hot.

4. Most stars come in multiples

It might look like all the stars are out there, all by themselves, but many come in pairs. These are binary stars, where two stars orbit a common center of gravity. And there are other systems out there with 3, 4 and even more stars. Just think of the beautiful sunrises you’d experience waking up on a world with 4 stars around it.

5. The biggest stars would engulf Saturn

Speaking of red giants, or in this case, red supergiants, there are some monster stars out there that really make our Sun look small. A familiar red supergiant is the star Betelgeuse in the constellation Orion. It has about 20 times the mass of the Sun, but it’s 1,000 times larger. But that’s nothing. The largest known star is the monster UY Scuti.  It is a current and leading candidate for being the largest known star by radius and is also one of the most luminous of its kind. It has an estimated radius of 1,708 solar radii (1.188×109 kilometres; 7.94 astronomical units); thus a volume nearly 5 billion times that of the Sun.

6. There are many, many stars

Quick, how many stars are there in the Milky Way. You might be surprised to know that there are 200-400 billion stars in our galaxy. Each one is a separate island in space, perhaps with planets, and some may even have life.

7. The Sun is the closest star

Okay, this one you should know, but it’s pretty amazing to think that our own Sun, located a mere 150 million km away is average example of all the stars in the Universe. Our own Sun is classified as a G2 yellow dwarf star in the main sequence phase of its life. The Sun has been happily converting hydrogen into helium at its core for 4.5 billion years, and will likely continue doing so for another 7+ billion years. When the Sun runs out of fuel, it will become a red giant, bloating up many times its current size. As it expands, the Sun will consume Mercury, Venus and probably even Earth. 

8. The biggest stars die early

Small stars like red dwarfs can live for trillions of years. But hypergiant stars, die early, because they burn their fuel quickly and become supernovae. On average, they live only a few tens of millions of years or less.

9. Failed stars

Brown dwarfs are substellar objects that occupy the mass range between the heaviest gas giant planets and the lightest stars, of approximately 13 to 75–80 Jupiter masses (MJ). Below this range are the sub-brown dwarfs, and above it are the lightest red dwarfs (M9 V). Unlike the stars in the main-sequence, brown dwarfs are not massive enough to sustain nuclear fusion of ordinary hydrogen (1H) to helium in their cores.

10. Sirius: The Brightest Star in the Night Sky

Sirius is a star system and the brightest star in the Earth’s night sky. With a visual apparent magnitude of −1.46, it is almost twice as bright as Canopus, the next brightest star. The system has the Bayer designation Alpha Canis Majoris (α CMa). What the naked eye perceives as a single star is a binary star system, consisting of a white main-sequence star of spectral type A0 or A1, termed Sirius A, and a faint white dwarf companion of spectral type DA2, called Sirius B. 

To know more click the links: white dwarf, supernova, +stars, pulsars

sources: wikipedia and universetoday.com

image credits: NASA/JPL, Morgan Keenan, ESO, Philip Park / CC BY-SA 3.0

St. Maria Goretti (1890–1902) was born in Italy to a humble farming family. Her father died from malaria when she was 9, leaving the family destitute. Her mother and older siblings worked in the fields while Maria managed the household chores and cared for her younger siblings. One summer day while the family was in the fields, Maria was attacked by their neighbor, a 19-year-old boy named Alessandro, who attempted to rape her. Maria wasn’t yet 12 years old. She fought back, yelling to him that it was a sin and that he would go to hell for his actions. In a rage over her refusal, Alessandro stabbed Maria fourteen times. Doctors operated to save her life, without anesthesia, and Maria lingered for two days after the attack. She verbally forgave Alessandro for his crime, offered her suffering to God, and died while holding a crucifix. Alessandro went to prison for murder, full of hardness of heart. One day in prison Maria appeared to him in a dream. She placed 14 white lilies, one at a time, into his hands; one for each of the times he stabbed her. This stunning experience of forgivness brought him to repentance, and Alessandro was converted. Upon leaving prison he sought reconciliation with Maria’s mother and with the Church. Alessandro called Maria “his little saint” and prayed to her daily. He also attended her canonization Mass in 1950. Alessandro joined the Franciscans as a lay brother until his death in 1970. St. Maria Goretti is the patron saint of children, youth, young girls, the poor, martyrs, purity, poverty, chastity, rape victims, and forgiveness. Her feast day is July 6th.

153 - A Narcissistic Number

153 is a narcissistic number–a number that can be generated from its own digits (so it’s obsessed with itself? hence the narcissism?) like so:

More precisely, a narcissistic number is a natural number that is the sum of its own digits each raised to the power of the number of digits. So since 153 has 3 digits, each digit is cubed and then summed together. There are only four 3-digit  narcissistic numbers:

A very interesting thing about narcissistic numbers is that, unlike may other sets of numbers (e.g., even/odd numbers, prime numbers, triangular numbers, etc.), there are only finitely many of them. In base 10, there are only 88 (10 of them being the 1 digit numbers). The largest narcissistic number has 39 digits, this guy:

115,132,219,018,763,992,565,095,597,973,971,522,401 

Why is this? Essentially, the sum cannot keep up with the size of the number. More info here: https://en.wikipedia.org/wiki/Narcissistic_number

A delightfully concise animated proof of the sum of the arithmetic progression of the naturals.

Mathematics is beautiful. <3

😶 [Twitter/DianeTurnshek]

“Patristic literature associates the timing of the Circumcision on the eighth day with the Resurrection. Here the argument rests on the kind of mystical numerology which we no longer take seriously, but it did formerly engage so great minds. The reasoning runs somewhat as follows. Seven is the number of completion and fullness, for the world was created in seven days, and is due to pass through seven ages. But if seven is perfect, then seven-plus-one is pluperfect. Eight, therefore, stands for renewal, regeneration - whence the architectural tradition of eight-sided baptistries. And Christ rose from the dead on the day superseding the Sabbath, on the eight day; just as the world’s seven ages will be followed in the eighth age by the General Resurrection. These notions attach themselves almost from the beginning to all theological meditation on Christ’s circumcision. From St. Justin Martyr in the 2nd century to St. Thomas Aquinas, it is the sense of the mystery that the Circumcision on the eighth day prefigures Christ’s Resurrection, and thereby, implicitly, the resurrection of all.”

— Leo Steinberg (The Sexuality of Christ in Renaissance Art and in Modern Oblivion, page 52). On the next page he quotes Bede, “[It is] our true and complete circumcision, when, on the day of judgment, all souls having put off the corruption of the flesh … we will enter the forecourt of the heavenly kingdom to behold forever the face of the Creator. This is prefigured by the circumcision of the little ones in the temple of the Lord in Jerusalem.”

“Inside every person you know, there’s a person you don’t know”

Perfection is not only the reason behind the passion but your hard work matters a lot for your passion.

S.S.K (via creativespacetime)