The goal of this blog is to create a list of super facts. Important facts that are true with very high certainty and yet surprising, misunderstood, or disputed by many. This blog aims to be challenging, educational, and fun, without it being clickbait. I determine veracity using evidence, data from reputable sources and longstanding scientific consensus. Prepare to be challenged (I am). Intentionally seek the truth not confirmation of your belief.
Super fact 64 : V – E + F = 2 is true for all convex polyhedra, where V is the number of vertices (corners), E is the number of edges, and F is the number of faces of a convex polyhedron. This is called Euler’s formula for polyhedra.
Polyhedron Euler’s formula. The cube has 6 faces, 8 corners (blue dots), and 12 edges (grey lines) and 8 – 12 + 6 = 2. Popular shapes Asset id: 2362684465 by ramonparaiba.
Convex polyhedra are polyhedra without holes, or it has no internal angles larger than 180 degrees. To express that exactly; A convex polyhedron is a three-dimensional solid with flat polygonal faces where a line segment connecting any two points on its surface or interior remains entirely within the solid. I can add that convex polyhedra consists of convex polygons as their faces. All its faces are convex polygons.
The difference between convex and concave polygons. Notice that the concave polygons on the right have “holes” in them, or inner angles larger than 180 degrees, and that you can draw a line starting and ending inside the polygon that goes outside the polygon.
It is easy to understand that there are an infinite number of convex polyhedra. All pyramids (with convex polygons for bottoms) are convex polyhedra whether the bottom is a square/rectangle, or a convex pentagon, hexagon, heptagon, octagon, or any kind of convex polygon, even with trillions.
A hexagonal pyramid (it is convex). Tomruen at en.wikipedia, Public domain, via Wikimedia Commons.
Examples of convex polyhedra are cubes, boxes, a tetrahedron, pyramids of various sorts, an octahedron, dodecahedron, icosahedron, but there are infinitely many.
As an example, take a cube (like a dice). It has six faces (F = 6), eight vertices (corners V = 8), and 12 edges (V – E + F = 2 or 8 – 12 + 6 = 2). A tetrahedron has four faces (F = 4), four vertices (V =4), and six edges (E = 6) (V – E + F = 2 or 4 – 6 + 4 = 2). A pyramid (with a square bottom) has five faces (F = 5), five vertices (V = 5) and eight edges (E = 8) (V – E + F = 2 or 5 – 8 + 5 = 2). An octahedron has eight faces (F = 8), and six vertices (V = 6), and twelve edges (E = 12) (V – E + F = 2 or 6 – 12 + 8 = 2). A dodecahedron has twelve faces (F = 12), and twenty vertices (V = 20), and thirty edges (E = 30) (V – E + F = 2 or 20 – 30 + 12 = 2). An icosahedron has twenty faces (F = 20), and twelve vertices (V = 20), and thirty edges (E = 30) (V – E + F = 2 or 12 – 30 + 20 = 2). Euler’s Polyhedral Formula works for all of them and for all the infinite number of convex polyhedra that exists.
Tetrahedron, cube, octahedron, dodecahedron and icosahedron, Shutterstock Asset id: 2138211027 by Dotted Yeti
I consider this a super fact because it is quite amazing and surprising that the number of faces, vertices, and edges follow the same formula for all convex polyhedra. At least it is surprising if you haven’t seen it before. I should say that Leonhard Euler’s most celebrated discovery is probably his discovery of the Euler Number and the associated Euler’s Formula.
More Polyhedra Examples
The three first examples below are convex polyhedra so Euler’s Polyhedral Formula apply. The last two examples are not so Euler’s Polyhedral Formula does not apply.
This is a truncated icosahedron, which is a convex polyhedra, so Euler’s Polyhedral Formula apply. Shutterstock Asset id: 2309812551 by Mima Subota.This Rhombicuboctahedron is an example of convex polyhedron, so Euler’s Polyhedral Formula applies. Cyp, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons.This Icosidodecahedron is another example of a convex polyhedron, so Euler’s Polyhedral Formula applies. Attribution must be given to Robert Webb’s Stella software as the creator of this image along with a link to the website: http://www.software3d.com/Stella.php. A complimentary copy of any book or poster using images from the Software would also be appreciated where feasible., Attribution, via Wikimedia CommonsThis hexagonal torus / toroidal polyhedron is not a convex polyhedra, so Euler’s Polyhedral Formula does not apply in this case. Tom Ruen, SVG version from de:User:Antonsusi, Public domain, via Wikimedia CommonsThis Merkaba Polyhedron is not a convex polyhedra, so Euler’s Polyhedral Formula does not apply in this case. Shutterstock Asset id: 1296063079 by Panimoni
Super fact 62 : Facts exist in science; a scientific “fact” is an observation of a natural phenomenon that has been repeatedly confirmed by independent observers and is accepted as true for all practical purposes.
Outside of mathematics and logic nothing is ever the final truth, not in science, and not anywhere else. However, there are facts that have been so well confirmed and are so basic that there is no reason to doubt them. Earth is not flat like a pancake, and the sun is a star, are two examples of astronomical facts. Most dogs have four legs is another fact. The speed of light in vacuum is the same for all observers is a fact in physics that is surprising if you didn’t know it before. Scientific facts are verified by repeatable careful observation or measurement by experiments or other means. It is possible that we are all living in a virtual reality, like in the movie The Matrix, and that Earth is really flat like a pancake after all, because all of reality is a dream. However, for all practical purposes, it is not the case.
This blog, super facts, deal with facts that are surprising, strange, or disputed by non-experts, and yet true because they have been verified, for example, in the case of scientific facts, by repeatable careful observation. Anyone is free to object if you think I am wrong about a fact.
My next super fact is going to be “Evolution is a fact”. Evolution is also a scientific theory, but it means something different from when you say evolution is a fact. Moreover, a Scientific Theory is not a guess, as commonly but incorrectly assumed. I am bringing this up because many people who are typically unaware of the evidence behind a fact will use arguments such as “science does not know everything”, “it is just a theory”, etc., in efforts to dismiss a well-supported claim.
I should say that this post is inspired by a Facebook post by “The Credible Hulk”, a Facebook page managed by a group of anonymous scientists opposing misinformation around vaccines, global warming, evolution and GMOs. I did not save the post, but it went something like this:
One of the commentors said : “Calling evolution a “fact” defeats your argument. The Theory of Evolution is by definition a theory not a fact. It’s the currently agreed upon hypothesis but not a fact”
What the commentor did not realize is that “Theory” in the context of science does not mean what he thought it did. I am using past tense because he got “schooled”. To his credit he did not respond with insults and neither did the Credible Hulk, which does not seem to be standard on Facebook. However, his comment illustrates something that drives scientists like those who created “The Credible Hulk” nuts, and that is the widespread lack of understanding of the difference between a guess, a hypothesis, a scientific fact, theory as used in common language and used when talking about a scientific theory.
Rather than having this discussion over at my upcoming “Evolution is a fact” post, I am making a separate post about it. I consider “There are Scientific Facts” a super fact because it is true, and yet the confusion around it and what a Scientific Theory pertains is massive, and it is an important topic.
What is Science?
Science is the process of learning about the world through systematic observation and experimentation to gain knowledge about how things work. It involves observing phenomena, forming testable ideas (hypotheses), systematic studies, conducting experiments, and collecting evidence and facts that support or refute those ideas, ultimately leading to a deeper understanding of general truths and natural laws. If an idea/hypothesis correctly predicts and explains facts, it becomes a theory, which is something that is very different from a guess.
The process of making observations, formulating testable hypotheses, conducting experiments, analyzing data, and drawing conclusions to understand phenomena and solve problems is referred to as the scientific method, and there are different types of scientific methods. Some involve experiments, other involve analysis historical artifacts or existing data. Objectivity, reproducibility, falsifiability, and predictive power or problem solving are essential.
Aspects of scientific research include analysis, data collection, sometimes surveys, development, establishing facts, creating knowledge, and data entry so that others can repeat it and verify results. Shutterstock Asset id: 1100776715 by Trueffelpix
What is a Scientific Theory?
When people hear the phrase “evolution is a theory,” many mistakenly assume it means evolution is just a guess or speculation. In science, however, a theory is far more than a guess. A scientific theory is an explanation of an aspect of the natural world that can be or that has been repeatedly tested and has corroborating evidence in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. In other words, it is a well-tested, comprehensive explanation of natural phenomena, supported by an extensive body of evidence.
Conceptual Illustration of Scientific Method and Knowledge Acquiring. Notice, not all scientific methods necessarily include experiments. Some include surveys, or testing of ancient artifacts, etc. Shutterstock Asset id: 2139402875 by TarikVision
The evidence for evolution is both vast and compelling. It is not just the massive fossil record, it is in DNA, anatomy, there’s geographic evidence, and evidence from dozens of other scientific fields, not to mention that evolution is directly observable. There is a Theory of Evolution, that is the well supported explanation for evolution, or evolution by natural selection. There is also “Evolution is a fact” referring to, for example, the fact that we can directly observe it. It is true for all practical purposes, and that does not mean that evolution stops being a scientific theory as well as a fact.
Afterword
Even though science is constantly evolving and our knowledge is evolving and sometimes our understanding and scientific theories on a topic needs to be updated, scientific facts exist. Some scientific facts are extremely unlikely to change. For example, Jupiter has multiple moons, galaxies exist, global warming is real and is caused by us, and evolution is a fact. Before you decide to dismiss such a fact make sure you know what “theory” means in science, and most importantly educate yourself on the relevant evidence. There might be a whole lot more than you imagined, and you may discover that the evidence you thought was contrary is not evidence.
You often hear “science does not know everything”. That’s true. If science knew everything it would stop. However, the collective knowledge created by science is enormous and as individuals we know next to nothing. So be humble and learn from scientific evidence presented by reliable sources.
Super fact 59 : Most people have heard of electrical charges, positive and negative. However, in nature there are also color charges—red, green, and blue—which are analogous to electric charges. In addition, there are anti-red, anti-green, and anti-blue charges.
As you may know, atoms consist of particles. Electrons surround the nucleus of the atom. The nucleus of the atom is in the middle of the atom and it consists of protons and neutrons. Electrons have a negative charge. Protons have a positive charge. Neutrons do not have an electrical charge. Electrons are so called elementary particles. They are not composed of other particles. Protons and Neutrons, on the other hand, are not elementary particles. They are composite particles consisting of quarks, gluons and quark pairs called mesons.
Four elements with a nucleus and electron shells. The number of electrons, protons, and neutrons is shown. The green particles circling the nucleus are electrons. The red particles in the nucleus (middle) are protons and the blue particles in the nucleus are neutrons. The colors of the particles in this picture have nothing to do with color charges. The four elements are Hydrogen, Carbon, Oxygen, and Nitrogen. There are 118 elements. These elements can combine into millions of different kinds of molecules that make up everything. Asset id: 1555863596 by OSweetNature.
Quarks have electric charges, just like an electron and a positron, which is why a proton has an electric charge, a positive electric charge. However, in addition quarks have something called color charge. Unlike electric charges, which come in two forms, negative and positive, they come in three forms red, green and blue and in anti-red, anti-green, and anti-blue (well six forms actually). I should say that the color charges, red, green and blue, are not real colors. They are just names. Just electric charges are associated with electric forces; color charges are associated with the nuclear strong force. The strong force is even stronger than the electrical force.
If you take an equal amount of positive and negative electric charges you get something that is electrically neutral. If you take an equal amount of red, green and blue you get what is called white, or neutral. If you take an equal amount of red and anti-red you also get white. Any other mix gives you a net color charge.
The proton and neutron each consist of three quarks. Protons consist of two up quarks and one down quark. Neutrons consist of two down quarks and one up quark. Both protons and neutrons have a net white charge. The yellow squiggly lines are gluons transporting color charge between the quarks. Asset id: 2333679305 by KRPD.
I can add that gluons are elementary particles that in many respects are like photons. Light consists of photons. It is because of the photons that we can see. In addition, the photons transport electrical charge. Photons are massless elementary particles with the intrinsic spin of one, and they belong to a group of elementary particles called Bosons. Gluons transport color charge, and they are massless and have an intrinsic spin of one and belong to the same group of elementary particles called Bosons. Unlike photons, they are stuck inside the nucleus and unlike photons they never get to see the light of day. The pun was intended.
Matter, light, and electrical charges are all part of our daily life. We can touch matter, see light, and we come across electrical charge when we touch something that is charged or when we see lightning. However, we do not come across quarks, gluons, and color charges in our daily life because they are hidden at the center of the atoms. Yet they are fundamental to the existence of matter, of us. We know color charges exist, the existence of color charges is an important fact, and yet it is not a well-known fact and often a big surprise to people. Therefore, I think it is a super fact.
The 118 Elements and the 3,500 Isotopes
There are 118 known elements. Why not 500, or just 4 or 5, like the ancient Greeks believed? Each element is defined by it having a certain number of protons and the same number of electrons if it is to be electrically neutral. The problem with having more than one proton in the nucleus is that protons all carry a positive charge and therefore want to push each other away. Same charges repel and different charges attract. What saves the nucleus from blowing apart are the neutrons and the associated strong nuclear force (protons & neutrons) which is guided by the color charges. The quantum model for electricity is called Quantum electrodynamics or QED. The quantum model for color charges is called Quantum chromodynamics or QCD.
As you add more protons it becomes increasingly more difficult for the nuclear forces (strong and weak) to hold the nucleus together. The positive charge of the protons is pushing too hard. That’s why there are only 118 Elements. Another thing to note is that the number of neutrons does not have to be the same as the number of protons. This means that for each element there are several kinds of so-called isotopes. For example, carbon has six protons and six electrons (if the atom is electrically neutral) but the carbon atom / element can have six neutrons, seven neutrons, or eight neutrons. You call them carbon-12, carbon-13, and carbon-14, where the number represents the number of protons plus the number of neutrons.
Three natural isotopes of Carbon Stock Vector ID: 2063998442 by zizou7This is a simplified Bohr model of the Uranium atom. There are 92 little blue balls circling a nucleus in the middle of the atom. Those are electrons. In the nucleus there are 92 protons. Those are the red balls with plus signs. In addition, there is a yellowish smudge around the protons in the nucleus. Those are the neutrons. Depending on the isotope, there are 143 neutrons for U-235, 146 neutrons for U-238 and 142 neutrons for U-234. Shutterstock asset id: 1999370450 by Patricia F. Carvalho
It is the electrons that determine the chemical properties of an element, and therefore isotopes with a different amount of neutrons are chemically identical. However, they are different with respect to properties that relate to he nucleus, such as radioactivity/stability, and of course weight. Also, when atoms combine into molecules their chemical properties change drastically, but again that is due to the rearrangement of the electrons. There are around 3,500 known isotopes, most of them radioactive.
What is a Quark?
To learn more about Protons, Neutrons, Quarks, Gluons, Color Charges, and Quantum Chromodynamics you can watch this 10 minute video below.
Super fact 57 : Half the World’s Population live within a circle that covers 2% of the world’s surface, or 10% of earth’s land area. This circle is often referred to as the “Valeriepieris Circle” or Yuxi Circle, and it is centered on southeast Asia.
This circle, has a radius of a bit more than 2,000 miles, and encompasses densely populated areas of East and South Asia, including major population centers like China, India, and Indonesia. The original Valeriepieris Circle was created by a teacher named Ken Myers in 2013 and was larger (radius 2,500 miles) than the more optimized circle created in 2015. In 2015, Singaporean professor Danny Quah—with the aid of an intern named Ken Teoh created a significantly smaller circle (radius 2,050 miles) that included half the world’s population. 4.2 billion people live in the Valeriepieris Circle, which is 5.6 times as many people as in Europe and 12.4 times as many people as in the Unites States.
I consider this a super fact because it is true, it is an important fact, and it is a surprising fact to those of us who have not come across this information before. It is an important fact because it impacts how we view our world. The circle is located far away from Europe and North America, in a part of the world that is rising quickly economically. The people in this highly populated circle have different cultures, music, literature and religions from the US and Europe. They speak different languages, and they play different sports, well soccer (the real football) is international but not as common in the Valeriepieris Circle as in Europe or South America.
Those among us who live outside of this circle, for example, in the United States or Europe, probably need to pay more attention to this half of world. Especially, if you live in the United States, it is easy to believe that the world is about us. The existence of this circle demonstrates that this view is not a realistic view.
The original 2013 map by Ken Myers, with the interior of the circle. Half as many people live inside the circle as outside the circle. However, it is larger and less optimized compared to the circle from 2015 below. This circle is NASA, Public domain, via Wikimedia CommonsDanny Quah’s 2015 circle, on a Lambert azimuthal equal-area projection. It should be noted that the fraction of the area of the circle to that of the globe is equal to its equivalent on Earth. Again, half as many people live inside the circle as outside the circle. From Wikipedia cmglee, jimht at shaw dot ca, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons.
Population of Southeast Asia
The countries that are part of the Valeriepieris Circle are, for example,
Each country’s size represents the size of the population in 2018. Each little square represents 500,000 people. All 15,266 squares show where the world’s 7,633 billion peopls lived in 2018 (now the world population is 8,244 billion people). Image from our World in Data. By Max Roser for OurWorldinData.org – the free online publication on the world’s largest problems and how to make progress against them.
Population Statistics
Most people know that in recent centuries the world population has grown almost exponentially but is now projected to level off sometime around the middle of this century. Europe is an interesting example. A thousand years ago Europe’s share of the world population was around 14.5%. Then came the scientific revolution and the industrial revolution and by 1900 it was 25%. As other countries around the world became industrialized Europe’s share of the world population shrunk, even though the population of Europe kept increasing, just slower. Now Europe’s share of the world population is 9%.
As countries become wealthier their population growth tends to slow down, not just in Europe, but around the world. The world’s population growth is illustrated by the image from Our World in Data below (starting 5,000 years ago, ending the year 2000) and the six minute YouTube video below from the American Museum of Natural History (starting 100,000 years ago and ending the year 2100). The YouTube video also shows the projected population decline beyond the year 2050.
Population per square kilometer. Source of the original visualization Klein Goldewijk, Beusen and Janssen (2010). Long term dynamic modeling of global population and built-up area in a spatially explicit way: HYDE 3.1. In the Holocene 20(4) 565-573. The original visualization was adapted by OurWorldinData.org
Super fact 56 : The Bermuda Triangle mystery is a myth. There is not a higher risk of disappearances in the Bermuda Triangle. To be specific, disappearances do not occur in the so-called Bermuda Triangle, or Devils Triangle, with any higher frequency than in other comparable regions of the ocean. The “mystery” of the Bermuda Triangle is largely a manufactured one, perpetuated by sensationalized accounts that often misrepresent the facts and downplay the role of natural hazards like storms.
The number of ships and aircraft reported missing in the Bermuda Triangle is not significantly greater, proportionally speaking, than in any other part of the ocean. The U.S. Coast Guard, along with NOAA, the U.S. Navy, Lloyds of London who pays out insurance for ships and aircraft lost/missing at sea, and other organizations do not recognize the Bermuda Triangle as a unique or mysterious geographic hazard. They emphasize that this is a highly traveled area where the losses are consistent with natural phenomena such as strong storms, the Gulf Stream, human error, and poor navigation, rather than any mysterious forces.
Considering all this, the number of disappearances and accidents is what you’d expect. The Bermuda Triangle isn’t any more mysterious than the Greenland square, the New Zeeland circle, or the Azores Octagon, that I just made up. I consider this a super fact because it is very likely true, and yet surprising to many people who are convinced that there really is a mystery. Furthermore, it is important because it is such a well-known myth.
The Bermuda Triangle: It is approximately defined as a triangle Florida, Bermuda, and Puerto Rico. There is no exact definition. Alphaiosderivative work: -Majestic-, Public domain, via Wikimedia Commons.
Bermuda Triangle Mysteries
Just because the risk of disappearances of planes and ships is not higher in the Bermuda Triangle, does not mean that there aren’t mysterious disappearances and mysterious phenomenon occurring in the Bermuda Triangle. Some notable disappearances are USS Cyclops (1918), Flight 19 (1945), Star Tiger and Star Ariel (1948–1949), and the Witchcraft (1967). However, there are mysteries and mysterious phenomena occurring all around the world.
One of the mysterious phenomena occurring in the Bermuda Triangle is ocean swirls, and rogue waves, and methane burps might be another problem, but it is far from unique to the Bermuda triangle, and there are no magnetic anomalies in the Bermuda triangle as often alleged.
Ocean swirls frequently occur all over the world with some famous hotspots for ocean swirls by the coasts of Japan, Norway, Italy, Scotland, and Maine, USA. The ocean swirls in the Bermuda triangle might be due to movement of water between landmasses and/or the Gulf stream, but this is under investigation. There are no known giant or permanent ocean swirls in the Bermuda triangle.
Ocean swirl allegedly in the Bermuda Triangle Asset id: 1158148882 by PHOTO JUNCTION
As mentioned, another mysterious phenomenon is methane bubbling to the surface of the ocean. However, as can be seen in the maps in this National Geographic blog post the source of these methane burps of death aren’t typical to the Bermuda triangle. The methane hydrate field in the first map of the National Geographic blog post is mostly outside of the Bermuda triangle stretching from Cuba and up along the Florida coast. The second map, the world map, shows that these methane hydrate fields exist all around the world.
Our Honeymoon in Bermuda
Below are some old photos from our honeymoon in Bermuda in August of 1991.
Super Facts 