Only 15 Types of Plane-Tiling Convex Pentagons Exist


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It has just been proven that only 15 types of convex pentagons exist that can tile the plane. Which implies that there just might be a single polygon (almost undoubtedly concave) that can tile the plane in a non-periodic manner (as do Penrose tiles; but PTs require two different figures, not a single figure).

(If you’ve ever played with regular pentagons, you have discovered that they can’t tile the plane without gaps or overlapping. The pentagons referred to in this proof are NOT regular. Here is one such example, taken from the article:)

a tessellation with pentagons

You can see many of the details at the following link.



Rescheduled Open House at the Hopewell Observatory: Saturday, June 24, 2017


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We had to reschedule the public open house and star party from May to June 2017 because of bad weather last month. You are all invited, and it’s free. The directions and many other details can be found at a previous post on this blog

(Just ignore the date, because it’s no longer 2016! The directions are long, and I didn’t feel like copying and pasting them here.)

Looking at a planetarium app set for 6/24/2017, I see that Jupiter and Saturn will be well-placed for viewing at sunset, and the entire Summer Milky Way will be overhead, allowing you to look at lots of deep-sky objects like globular clusters, planetary and gaseous nebulae, open clusters, as well as distant galaxies. If you stick around until 4 AM, extremely bright Venus will rise in the east. The Moon will be too close to the Sun to be visible.

Caveat: we do not have running water, so no modern lavatory. We do have bottled water, an outhouse, electricity, and hand sanitizer. This place is really in the middle of the woods, which is where lots of insects and other arthropods live, so keep that in mind. We do have some bug juice you can use, but keep any spray far away from the telescopes!

If you have a telescope of your own, or binoculars, feel free to bring them. A flashlght or headlamp will be useful. We prefer red light at night, since white light makes you night-blind for about 10-20 minutes. If your flashlight(s) put(s) out white light, we have red plastic, tape, scissors, and rubber bands that you can use to shield your light.

Two Simultaneous ‘First Lights’ at the NCA-CCCC Telescope Making Workshop


Oscar Olmedo and Jeff Dunn both took the opportunity of a clear night last night to achieve first light with the telescopes that they have been working so hard on. The target was Jupiter. The location is right outside the Chevy Chase Community Center, and time was just about 10:00 pm. The fact that you can see so much in this iphone image shows that light pollution is a real problem there.


We also managed to do a star test using an artificial star on Oscar’s 6″ f/3. I made the testing rig with considerable help from Alan Tarica and Bill Rohrer. We reflected the light off of a known optical flat so as to double the testing distance. We had everybody in attendance at the telescope=making workshop examine the inside- and outside-of-focus images, and we all agreed that using the images in Richard Suiter’s book, it’s a bit overcorrected, probably somewhere near 1/4 wave of green light, which was what we were using — a green laser pointer attenuated and stopped down to about 100 micron hole. But good enough.

Next step for Oscar is to aluminize his mirror in our vacuum chamber.

Congratulations to both gentlemen!

Religions based on … well … myths, or alternative facts. Or lies.


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Every single religion that I can think of seems to be based on totally unreliable witnesses and stories that are mis-remembered (at best) or deliberately distorted.

Judaism just celebrated one of its most important rituals, the Passover seder, in which I have participated about six times. If you’ve forgotten, the story is supposedly recorded in the Old Testament (or Tanakh) and the event celebrates the freeing of a large group of Hebrew people from Egypt. They then wandered the Sinai desert (a very, very hot and dry place – I lived next to it for about 9 months).

The problem is, there is absolutely nothing in the historical record that corroborates any of this story. The Egyptians kept a lot of records, and much of it is still readable — no mention of any such tribe fleeing, no first-borns murdered, no special heavenly plagues, yadda, yadda. No archaeological evidence whatsoever of any tribe of Hebrews wandering in the Sinai desert for any such expedition.

(Stuff like that gets preserved there! In fact, at the famous fort and palace known as Masada, near the Dead Sea, you can clearly see the streets and walls of the camp built by the legions of the Roman Army that besieged and eventually captured the fort, from roughly 2000 years ago! Now THAT incident and war is definitely mentioned — in Josephus, among other places…)

That story of Abraham getting ready to slit his son’s throat and god providing a lamb instead? Really? Inscribed tablets from Mount Sinai – really? How do we know any of this? We don’t. And in any case, if God tells you to commit genocide (it’s spelled out in Genesis / BeReshit), is that a wonderful thing? I don’t think so.

If we get to Jesus, well, again, the evidence that he produced any miracles or was somehow resurrected and became one with God (or didn’t) is pretty darned thin. Today is supposedly the day that he got crucified (the Romans were NOT nice people!!!), which was a shame. The Romans killed and tortured and enslaved a LOT of people. I’m not so sure that they should be held in such high esteem…

But I can think of many ways that a body can be taken out of a tomb, and none of them involve miracles or angels. Then, if you read all of the various Gospels, canonical or not, you realize that their outlooks and details are all profoundly at odds with each other.

If you come to Mohammed, I can think of many ways that somebody could appear to be possessed and to recite various lines of poetry (see Mormons, below) — although that would certainly explain why he would have prophecies that justified what he wanted to do (such as marry little girls) or needed to be amended (see Satanic Verses…)

Now both Jesus and Mohammed said some stuff about equality and supporting the poor, nonetheless the leaders of both religions (Popes, Kings, Emperors, Califs and so on) ended up being wealthy beyond anybody’s dreams, while the majority of people lived in pretty base poverty….

If you go back to the founding of Buddhism, what does that mean that someone is ‘enlightened’? How do we know if someone is in fact in that state? Is it even a good thing to attempt to achieve it? It seems to me that it’s more worth while to try to be good to other people (without endangering your own welfare unless absolutely necessary) and to try to leave the entire planet (and solar system) a better place for your descendants — by not driving species to extinction, not raising the global temperature if at all possible, and by helping so many billions of our kin to avoid lives of infernal poverty and oppression.

Hinduism seems to blame the poor and lowest classes for having been wicked people in a past life, and therefore should be not permitted equality with the upper castes. Sounds great if you are a Brahmin, but what an oppressive religion, really! And how can anybody with an ounce of skepticism believe any of those stories?

Going back to 2000+ years ago — All those stories that the Romans, the Greeksm the Babylonians, Persians and Egyptians made up about their gods — are you serious? They actually believed that? Well, you may as well believe in the Tooth Fairy or the Easter Bunny or the Flying Spaghetti Monster!

Oh, can’t leave out the Mormons. Golden plates buried in upstate New York but only viewable and translatable by someone talking through his hat, writing pseudo-king-James-English and talking about lots of animals and plants and metals that supposedly were used by warring tribes of American Indians — and nobody has ever found figs, wheat, camels, sheep, goats, or horses, or the use of iron or wheeled vehicles of any sort anywhere in the Americas for the entire period of say 500 BC to 1491. So that’s all a lie, too.

Sorry if I offend you, but while I know I’m not perfect (far from it) I don’t need fairy tales to try to be a better human being. I prefer to know things that are true and verifiable. And I really don’t like it when people try to kill each other to support ideas that are really just hoaxes.


How Britain Became an Island


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Interesting report with pretty geological maps indicate that the Island we call Britain got cut off from what we know as France and Belgium by a catastrophic waterfall and flood that broke through what we now call the Straits of Dover as the ice that covered Northern Europe was beginning to melt, and sea levels were much lower than today.


Here is the link

By the way, if the weather is fairly clear, it’s easy to see the famous White Cliffs of Dover from the French side (for example, at Cap Gris-Nez).