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I was so happy to see the students again! Or, as Arjun calls them, "the big kids." He thinks they are the coolest. They are, really. Though they are not all so big.
The first finished project of the year is the Kindergarten shapes game project. Kindergartners spend most of the year in Art looking at the work of abstract expressionists. We start off by looking at and talking about simple shapes. I read them this book:
I love this project. I love it even more every time I see the results. They are so different every single time!


Hello everbody, this year we are ready to tell you new stories about UP SCHOOL
A typical Tuesday
Today the first subject is math and we do algorithms. We finish with multiplication strategies. The second subject is Italian and we study the difference between plural and singular.
Then we have a break and we eat an apple. Then we go to the garden and we play volleyball. After that we work on the blog and we write this article. Then we have lunch. After lunch we have Italian again and we finish the day with reading and studiying
After the four o`clock break we go home.


In this chapter, we find the quintessential link between the three-dimensional geometries of the CU and the harmonic, mathematical “frequency numbers” of the Octave.
This link comes to us through the work of Mr. Carl Munck. We will see how Munck discovers that all of the “Gematrian” frequency numbers that indicate sound vibrations have only two commonly shared tangents.
He then shows how the Speed of Light, in seconds, is a precise function of these same two tangents. This gives us a solid background upon which to establish a fundamental mathematical connection between light, sound and geometry, adding great weight to the reality of this theory, and therefore the reality of Ascension as well.
PART ONE: SO WHAT IS A DIAMAGNETIC VORTEX, ANYWAY?
Since we have been looking at Dr. Richard Lefors Clark’s “bowtie” shaped vortices in great detail, it is important for us at this point to make mention of Dr. Clark’s theories of diamagnetism and magnetic null zones.
After all, the Wilcock reading in Chapter 17 suggested that these energy forces had a lot to do with the siting of ancient monuments. This was given as the “answer” that would rectify the positioning of certain stone and earthworks in Munck’s system with a mappable, planet-wide grid system.
According to Dr. Clark, the newest advances in the science of magnetism have shown that there is a positive / negative polarity reversal that occurs in the center of a magnetic field (see below diagram.)
It is at this point, called a “Bloch Wall,” where the spiraling energies of the north pole meet the spiraling energies of the south pole, and they overlap. At the overlap point, we get the “bowtie” shape that we see on Earth in the above examples.
The point of magnetic flow reversal, or the “Bloch Wall,” creates what we now term as anti-gravity, nulling its effects and / or changing its direction. Dr. Clark shows in Anti-Gravity and the World Grid how magnetic scientists have actually studied and measured this “Bloch Wall” phenomenon using electromagnets.
As we look at the above illustration, we should keep in mind that the lines on the Global Grid provide the organization for these spinning magnetic fields. In other words, the lines on the Grid are flowing like rivers, due to the spiraling nature of the energies that make them up.
And thus, if we look back to the diagram of the Bermuda Triangle vortex, we can see that the north-south vertical line that intersects Grid Point 18 next to Florida would be the “organizer” for the magnetic energy flows. Then, the magnetic polarity will reverse at the exact center of the bow-shaped area.
It is here that we will get our “Bloch Wall” effect produced, then causing the Bermuda Triangle anomalies, as well as providing exceptional spiritual energy. It is no surprise that many people will want to go to Florida to retire – the youthful energy explodes in abundance there!
If it were truly possible that the Earth’s magnetic field could produce such spirals of energy, then we should expect there to be places where it would be very evidential that something anomalous was occurring.
Certainly Sanderson’s work on the “vile vortices” like the Bermuda Triangle satisfies this, as does Munck’s mention of the anomalies surrounding Rock Lake in Wisconsin. There is another area that also obviously falls under this effect, and that is the area known as the Oregon Vortex.
William Childress featured the Oregon Vortex in an article for the industrial newsmagazine “Compressed Air,” which has been circulating in print for over 100 years.
As this is a reputable, mainstream scientific journal, it would be unlikely for them to print a study that was considered to be “fringe” science. Instead, it appears that their investigation of this vortex came from a genuine interest in trying to uncover and understand anomalous Earth phenomena.
Childress’ article starts out by describing the most crowd-pleasing feature in the Oregon Vortex / House of Mystery. A 100-year old shack was built over the vortex, and within this shack, a broom is “standing rigidly straight in the middle of the room, untouched by anyone or anything, as if it were a spear stuck in the middle of the floor.”
The record time for the broom to remain standing, according to those who run the House of Mystery, is 36 hours! Again, we see the harmonic numbers emerging, this time in the number of hours involved. In another area of the House of Mystery, a golf ball is placed at the bottom of a trough, and it will roll uphill when released.
On the “Superman Platform,” a person can lean very far forward without falling, and thus appear to look like Superman in flight.
Other stunts that are demonstrated at the Oregon Vortex include height discrepancies, where two similarly tall people will walk in opposite directions and have noticeable and opposite changes in their height.
A similar effect is demonstrated when a long plank is placed across two seven-foot tall posts; on the south end, the plank appears to be higher by a good three inches.
According to Childress, “in some way still not understood, a kind of “gravity warp” appears to make vertical objects taller or shorter as long as they are in the force field.” If we think about this on a much larger scale, we can visualize the expansion and contraction of landmasses, producing the structures that we have been examining above.
What is actually most interesting to us is the effects that are reported at the area called the “Vortex Post.” As Childress indicates, “people standing next to the post tend to sway in a circle like some bottom-weighted toy.”
From this piece of information, we can indeed see the spiraling nature of the gravitational fields at work! Also notable is a passage in Charles Berlitz’s Bermuda Triangle where there were reports cited of mariners encountering spiraling motions on their compass that became faster or slower depending on how close they were to the center of the vortex.
At these certain times, the spiraling energy from the vortex was actually stronger than Magnetic North, and overtook the normal operation of the compass.
It is also interesting that the owners of the Oregon Vortex / House of Mystery do not permit video cameras. They did not explain to Childress why this was so, only stating that regular cameras were permitted.
This falls perfectly in line with the Rock Lake information from Munck, and shows us that these vortices repetitively show their effects on electronics. We again remind the reader of the similar effects demonstrated by the UFOs in thousands of sighting reports.
Anyone who wishes to actually go out and see the Oregon Vortex for themselves can contact them through the following information: Oregon Vortex / House of Mystery, 4303 Sardine Creek Road, Gold Hill, OR 97525, (541) 855-1543. The tours are open from April through October.
And so, with the addition of physical information to back up the diamagnetism theories of Dr. Richard Lefors Clark, we have to consider that there is more to the Global Grid than just straight lines.
We have pieces of evidence like the bow-shaped structures of the landmasses indicated above, and now the spiraling, anomalous gravitational effects that can be seen in various spots. Although the above diagram of the diamagnetic field was drawn in two dimensions, Dr. Clark makes careful notice of the fact that these lines of force are indeed three-dimensional spirals.
These spirals are very important to study, as they form the basis for all of the Platonic Solids that we have spent so much time discussing. And looking in again on the extended version of the “Triple Julia Set” formation from 1996, this can clearly be seen:
PART TWO: SIMPLE, HARMONIC RELATIONSHIPS
In earlier chapters, we discussed how these universal spirals of energy generally fall into two main categories; namely, the square root of 2 and phi.
One of our postulates is that Nature, or the physical world that we can see, will show us all of the secrets in the metaphysical world.
Therefore, these spirals are not only simple mathematical concepts in our own dimension; they reach their fruition in the functions of the dimensions.
Now that we can see these spirals in action, mapped out for us by the Global Magnetic Grid and its effect on the shapes of continents, we can explore how each of the Platonic Solids “fit in” to these spirals.
As is written in Robert Lawlor’s book Sacred Geometry, the Platonic Solids are in a “simple harmonic relationship” to each other. As we can see in Table II below, that simple relationship is expressed in terms of phi and the square root of 2 in spiral form.
Lawlor gives us a complete breakdown of the Hindu “spectrum” of shapes, with the harmonic proportions for each one of them. The measurements listed are comparisons of the length of each side of the Platonic Solids.
Since every line on any Platonic Solid will be the same length, these measurements are the universal standard for each shape.
|Central Icosahedron||1 / phi2|
|Dodecahedron||1 / phi|
Table II. Harmonic Proportions of Platonic Solids.
In order for these proportions to be established, the researcher must determine where the “1” is going to be. We must remember the simple fact that if you have a square, and each side has a length unit of 1, the diagonals will measure out to the square root of two.
Similarly, if you assign a unit value of 1 to the diameter of a circle, the circumference will measure out to pi, or 3.14159 units. In order to compare the Platonic Solids to each other, we also need to assign a straight value of 1 to the sides of one of the shapes.
In order to have the basic harmonics work out simply and perfectly, the value of 1 needs to be assigned to the length of the side of the cube. All other proportions as indicated above represent the exact numerical value that we receive when comparing their lengths against the cube.
As we are on the subject of phi, it is also interesting to point out here that the “solar number” of 666 and the “lunar number” of 1080 also express the phi ratio when divided into each other.
John Michell’s work shows how many ancient monuments used these proportions, and we also see it in nature as well, being the harmonic relationship between such things as the size of planets. Since phi seems to be of such penultimate importance, we can see yet another reason for why the Hindus ascribed such religious significance to Purusha, or the icosahedron.
Now that we can see the actual mathematical structure of the spiraling energy that makes up the CU, we no longer need to wonder about whether they are, in fact, crystallized frequencies. We have seen it on the planetary level, and now we can see it on a mathematical level as well.
Hoagland’s team made the connection between these geometric shapes and the frequencies of the dimensions, and many might wonder exactly how he did that. The answer to that question actually helps us even more in understanding the true physics behind these harmonic, geometric shapes.
On his website, Hoagland has printed an early essay that he composed on hyperdimensional physics back in 1989. In this essay we have the clearest picture of how the Enterprise Mission team tied together the physics of higher dimensions with the abstract concept of Platonic geometry. This article is also located at www.lunaranomalies.com/Message.htm.
The “Message of Cydonia”
First Communication from an Extraterrestrial Civilization?
By Richard C. Hoagland and Erol O. Torun
Copyright (C) 1989 All Rights Reserved
[We are only going to reprint the part of this article that directly concerns us here.]
…If in the “Cydonia tetrahedral mathematics” we are truly seeing the deliberate communication of demonstrable astrophysical effects of a long-sought “Unified Field Theory,” this in itself would be remarkable confirmation of current efforts to discover such fundamental mathematical connections between Nature’s elemental forces.
For, most provocative: one leading mathematical approach to successfully modeling such connections is essentially based on a tetrahedral model, and a resulting mathematical expansion into “higher-dimensional, n-space relationships” (recently discovered) between the five Platonic solids (Sirag, 1989).
It is very important to note here that Mr. Saul-Paul Sirag, referenced below, has referred to ALL of the Platonic Solids in his model of “higher dimensions,” not just the tetrahedron. The work of Tony Smith also built upon Sirag’s geometric models, and a direct reference to Sirag’s work is made on Smith’s website.
In particular, these studies relate tetrahedral geometry as being topologically equivalent to three-toruses — tori extending into “one more dimension than our familiar three.”
[Many current efforts in pursuit of “unified field models,” such as the much-acclaimed “super-string theory,” routinely involve up to ten mathematical dimensions. Some more recent theories are exploring twenty-six (Sirag, ibid).]
As we have already stated in previous chapters, by breaking the “symmetry” of the strings in Superstring Theory, we arrive at an octave-based, 8 or 24 (8 x 3) – dimensional universe. This lines up with Srinivasa Ramanujan’s “modular functions.”
Phrased in simple terms:
The routine mathematical representation of vorticular flow in more than three dimensions — a three-torus — by means of three-dimensional tetrahedral models, opens up the possibility that the demonstrable geophysical effects of the “Cydonia tetrahedral message” are attempting to communicate the reality of additional dimensions (as opposed to mere mathematical abstractions) — and the observable reality of vorticular energy flow between adjoining “n-spaces.”
So, if we plug in our own discoveries in this chapter to what Hoagland and Torun have said here, and use the language that they expressed it with, Dr. Clark’s bow-shaped “diamagnetic energy vortices” would be another physical example of “the observable reality of vorticular energy flow between adjoining “n-spaces.””
Hoagland’s hyperdimensional physics asks us to visualize the spiraling energies making up the shapes themselves as being connected together to form a three-torus, which really is nothing more than what you would see if you removed the tetrahedron from the intersecting, spiraling lines that formed it.
When a number is assigned to a torus as in this case, it refers to how many visible “sides” the curving line produces. Thus, a three-torus is essentially like a triangular knot in its appearance.
Such totally unexpected (to non-specialists) and remarkable mathematical correlations — between as yet unpublished theoretical work into Unified Field Models, and the specific tetrahedral geometry apparently intended at Cydonia — gives added confidence that such a linkage was in fact intended. If so, there may be an additional confirmation of such a radical “Cydonia Unified Field Model”–
In the continuing, puzzling departure of some celestial objects from strict “Newtonian” mechanics.
And now, we check in on the References section to get a clearer picture on Mr. Saul-Paul Sirag:
Mr. Saul-Paul Sirag, for furnishing important references linking tetrahedral mathematics with “two and three-torus topologies,” and for providing examples from his own research of not only Schuster’s Hypothesis as potentially applicable to a Unified Field Model — but for specifically referencing tetrahedral mathematical topology and the Platonic Solids as directly applicable;
And finally, Mr. Stan Tenen (The Meru Foundation), for introducing us to Saul-Paul Sirag, for furnishing examples of his own research into the historical importance of the Platonic Solids (tetrahedra, in particular), and for valued general discussion of some of the more controversial aspects of our work.
[Note: Schuster’s Hypothesis relates to more recent published material from The Enterprise Mission regarding the energetic flow between bodies in the Solar System.]
It is important to point out here that the work of Stan Tenen, often referred to by Hoagland, gives us yet another layer of depth to explore in these matters. Tenen has discovered that the Torah, or the section of the Old Testament that was apparently dictated to Moses by God, has precisely encoded the formulae for constructing the Platonic Solids in its passages.
From this same Biblical scripture we also see the bizarre synchronicities that emerge with apparent mathematical certainty in the work of The Bible Code, explained in the book by Michael Drosnin of the same title.
(The Bible Code appears to have given us written prophecies of events 2000+ years in the future, in our own modern era. Drosnin’s biggest “claim to fame” with the Bible Code was the precise prediction of the assassination of Israeli Prime Minister Yitzhak Rabin.
The perfection of the mathematics involved in this, and the fact that it does not show up in any other books of the Bible, has excited mathematicians worldwide. It obviously helps strengthen the faith of Hebrews in the Torah as well!)
The work of Stan Tenen, showing us the mathematical encoding of the Platonic Solids within sacred text, gives us yet another interesting clue as to how the physical fundamentals of Universal Law and hyperdimensional physics were preserved as knowledge for us to use by Higher Intelligence.
Obviously, Tenen’s work is another major area of inquiry, and we leave it up to our readers to investigate the Meru Foundation on their own at the Meru website.
The one point that we need to mention here is that Tenen’s work also shows us a very interesting principle at work in the formation the Hebrew alphabet. Tenen explains that the Hebrew alphabetical characters represent different shadows of a single geometric figure.
That single geometric figure is, believe it or not, a spiral shape contained within a tetrahedron!
As amazing as it must seem, all we have to do is rotate the tetrahedron into different angular positions and then draw the shadows that result. All of the Hebrew letters will show up in a quite natural progression as a result of doing this.
We remind ourselves that the science of Gematria also started out in the Hebrew language, giving each of these tetrahedral rotations, or alphabetical letters, a sequential number.
The founders of this science seemed to have full awareness of the frequency numbers that underlie the dimensions, as well as their meanings. We remember as one example that 144 was said to equal Light, and now we can see through the work of Bruce Cathie that light speed, in harmonic terms, is indeed 144.
And now, we can see that the same authors of Gematria also knew of the Platonic Solids, as well as the fact that they have an inner, spiraling nature! The actual structure of the Hebrew alphabet was intended to show us this.
If we look back to the work of Carl Munck, we can see that the Ancients were very much concerned with the traditional English inch, foot and mile measurement when building their sacred sites. The work of John Michell, which we have not explored in detail here, also shows very significant relationships of the Great Pyramid and Stonehenge to the inch / foot / mile system.
We also remind the reader that the Sumerians gave us the Constant of Nineveh, and that it was a value expressed in seconds. We also remind the reader that the Speed of Light, in conventional terms, is also expressed in miles per second.
In the chapter on Bruce Cathie, we demonstrated how the harmonic of Light shows up precisely when we solve the Speed of Light for (x) minutes of arc per grid second. The value that we end up with is 144,000 minutes of arc per grid second for the speed of light in free space.
This puts it into the simple harmonic terms that the Universe works off of, and that the minds of the ETs navigating our globe can understand. Now, we can see here that the values of miles and seconds are also important in harmonic terms as well, to the Atlanteans and their cohorts.
So, we wonder to ourselves, could the Speed of Light also have harmonic significance when expressed in miles per second?
We do find that this is indeed the case. Not only that, but it ties in directly with the science of Gematria, which we have just been re-examining here.
It also ties in with the work of Carl Munck, our pioneer archeocryptographer who discovered a universal coordinate system being used within all sacred sites worldwide. It also ties in with the fundamental, spiraling nature of the geometric forms that the authors of the Gematrian sciences were very much aware of.
Carl Munck was studying the Gematrian “frequency numbers,” and started to notice that there was a definite mathematical redundancy to them. The redundancy came when he started calculating the tangents of each number, and found out that they were all the same!
If we remember from trigonometry class in high school, the tangent function is used to measure the intersection between a straight line and the very edge of a circle. This also could obviously be the intersection of a straight line and a curve as well, thus mapping – you guessed it – a spiral.
We now go directly into a reprint from Mason et al.’s Gematria page, which explains this point, and eventually tells us how these numbers harmonically tie into the Speed of Light, measured in miles per second. Here is Mason et al. to explain.
Carl figured a certain logic was demanded by these [Gematrian frequency] numbers, so he arranged them into two separate scales, organizing them by their tangents, and marking the numbers that came from the ancient systems with asterisks (*), and filling in the “blanks,” with appropriate numbers, something like this:
In the newsletter, Carl had a longer list of these numbers in vertical columns. He also drew in sine waves connecting the numbers, which seemed to be suggested by their logic.
He noted the consistent differences between the various numbers in the top two rows of 36 and 144, such as 108 – 72 = 36 and 252 – 108 = 144. The differences between the bottom rows are 108 and 72, such as 144 – 36 = 108; and 216 – 144 = 72.
The suggestion of sine waves, Carl said, is very, very obvious. Did the ancients know about sine waves? Did they have oscilloscopes? Were they suggesting a certain frequency?
PART THREE: A FREQUENCY OF LIGHT
Carl was shocked when he multiplied the two Gematrian tangents:
3.077683537 x 0.726542528 = 2.236067977
He knew that 2.236067977 is the square root of five!!!
That’s the pyramid codex talking!”, Carl says. He asks, “Why does the square root of five answer the sine waves of the Sacred Numbers? What was the reasoning behind it?… [The reasoning was that] the square root of five is itself a Tangent; the Tangent of 186234.09485, which is the speed of light in air!!!
Carl points out that the speed of light in a vacuum is 186282.5894 miles per second, but when light travels through air, it is slowed down to 186234.09485 miles per second. Enter this speed-of-light-in-air number into your calculator, and then press the tangent key, to see that it is very close to the number arrived at by multiplying the two Gematrian tangents…
[Here we remind ourselves that the tangent is a mathematical function that can be used to map out a spiral. The Speed of Light has a tangent of the square root of five, and this in turn has a tangent that harmonically relates to ALL frequency numbers making up the light / sound / geometric structure of the Octave of dimensions. You simply multiply their two commonly shared tangents together to get this number.]
Carl concludes –
And there we have it, the reasoning behind the Sacred Numbers of Gematria, the same ones preserved in eastern metrology and western calendrical computing; square roots and tangents – all keyed to the terrestrial speed of light.
It is delivered through the pyramid codex in nearly the exact methodology they used in keying the earth’s equatorial circumference to the cube root of double-pi when they built the Great Pyramid at Giza.
Munck’s work quite well explains how the Great Pyramid was built to unify the Earth’s circumference at the equator with the “constant” of the cube root of double pi, and it is also explained on Mason et al.’s Gematria page, from which this was excerpted.
No communications across ancient oceans? No prehistoric writing that makes any sense? Ignorant stone age progenitors? I’m afraid I’m not buying anymore, not when I can so easily find this kind of mathematical evidence to the contrary.
Someone back there had it all; maps of enviable accuracy, a complete knowledge of every inch of our planet, a thorough understanding of mathematics and, yes, even calculators and computers we take for granted today — because without such tools, they could never have put it all together.
Why do I say that? Because the U.S. Geological Survey advises me that they have the only computer in the United States which is programmed to calculate accurate distances between widely separated points anywhere on the planet — which means — that before the ancients could have marked out the pyramid grid system, they required a computer of the same caliber!
And so, from this excerpt, we can see very clearly how Carl Munck has discovered a similar harmonic function for the Speed of Light in miles per second, as Cathie did in his own harmonic system.
The most amazing point of all was not addressed by “The Code Gang” in this article, though, and that is the centering on the square root of five as being so important. What we see, when investigating Robert Lawlor’s book Sacred Geometry, is that the internal measurements of all the Platonic Solids are a function of phi, square root of two, square root of three and square root of five.
And so, the connection is obvious — the hidden mathematical properties of light reveal that it is traveling in a spiral formation, which is exactly what Ra tells us in the Law of One series. These spiraling lines or “superstrings” in the sea of energy known as the “aether” then form the framework for the different Platonic Solids.
Remember that we just showed above how the lengths of the sides of the Platonic Solids can all be expressed in terms of phi and the square root of two. However, a cube with a side length of 1 will have a diagonal of the square root of two on each of its faces, and if you draw a diagonal through the center of the cube between two points, its value is the square root of 3.
In addition, when we measure the diameters of these shapes, and their harmonic relationships, one of the most important ratios of all is indeed the square root of five. In Lawlor’s words,
The square root of five is the proportion which opens the way for the family of relationships called the Golden Proportion, [or the phi ratio.] The Golden Proportion generates a set of symbols which were used by the Platonic philosophers as a support for the ideal of divine or universal love.
It is through the Golden Division that we can contemplate the fact that the Creator planted a regenerative seed which will lift the mortal realms of duality and confusion back towards the image of God.
So, the connection of the square root of five to the Platonic Solids is the fact that the phi ratio grows directly out of it. Now we can see from the work of Carl Munck that the Speed of Light is also directly a function of the square root of five, and furthermore that the square root of five is directly a function of the Gematrian Numbers.
This is the cornerstone that we have been waiting for. We have already expressed the harmonic link between these “perfect” harmonic numbers for the vibrations of sound in air. These “perfect” numbers only come about when we measure them against one second of time as we now have it.
If our seconds were shorter, the harmonic ratios would still be preserved, but they would not be whole numbers any longer. It appears that the second of time that we now use from the Sumerians gives us perfectly round numbers for the vibrations of each note in the Octave.
This alone suggests a high level of scientific knowledge that went into this apparently archaic system of measurement. That only further strengthens the case for why we will see in later chapters that they also formulated the Constant of Nineveh, a number that allows all planetary orbits to be quickly calculated, as being expressed by a value in seconds.
It is only with the second that we now use that these frequency numbers are all round and rational. And, that second of time is a precise harmonic breakdown of one Earth day of 24 hours of 60 minutes with 60 seconds each.
We know that the Gematrian Numbers are all based on the number 9 as a foundation. Cathie showed us that if you convert our time units from a ratio of 8 to a ratio of 9, at 27 “grid hours,” then we have a measurement of “grid seconds” that shows us the harmonic “frequency number” of 144 as the Speed of Light in free space. We also see the “frequency numbers” coming out much clearer in the division of the number of Grid seconds per day.
So, in short, we now have a quite sufficient amount of scientific proof to show us that the Platonic solids are indeed a function of the mathematical expansion and contraction of curving superstrings in a spherical energy field, forming natural shapes such as what Hoagland would refer to as a “three-torus” when constructing a tetrahedron, for example.
This same information regarding spiraling lines of light was revealed to us by Ra and other sources, and now we have gone in and directly seen it mathematically. These superstrings travel at the speed of Light, and now with the work of Cathie and Munck we can see how the spirals themselves are functions of Light.
The harmonic frequency numbers, expressed in Gematria, are completely woven into this “fabric” of space and time.
So, what we essentially have here is a bullet-proof mathematical design that incorporates all of these various points together. We can see how these consciousness units function in their “inward coalescing” capacity by their effects on a planetary energy field.
Just as Ra told us that the consciousness units’ inward expansion creates gravity, so too do we now see with the Becker / Hagens grid that gravity demonstrates in a quite literal fashion how these various Platonic shapes emerge. The actual lines of force created by the shapes have a direct effect on the shaping of continental landmass.
Further information has now come our way regarding a direct mathematical connection between Platonic geometries and the harmonic number sequence.
As we briefly mentioned before, at the end of a MUFON conference in 1997, Richard Hoagland gave a sneak-preview of unpublished research that revealed that the orbit of Mars had once been exactly 666 Martian days in length, which is a clear harmonic number.
We already know that the Earth’s orbit could well have been 360 days exactly at some point in the past, and that this might be one explanation for why we have used 360 degrees in a circle.
So, Enterprise Mission associate Erol Torun decided to see what would happen if 666 degrees were used in a circle instead of 360.
They already had a collection of all the significant angle relationships between the various sections of a tetrahedron circumscribed within a sphere, and with few exceptions these were decimal-point values. Hoagland revealed that when 666 degrees are used, all of these values become whole numbers!
In the table on the next page, we have demonstrated this with our own calculations, based on Hoagland’s suggestion.
The first column shows the tetrahedral angles in a 360-degree system, the second column shows what the exact figure must be to harmonize with a 666-degree system precisely, the third column shows the value in the 666 system and the fourth column indicates how “harmonic” the 666 value is.
As we can see from the chart, the more “Y’s” there are, the more harmonic the number is, and the more N’s there are the more non-harmonic the number is. If we look at the column of Y’s and N’s, we can see that a clear waveform is visible. [No information was available on our harmonics chart regarding the last number, hence the NA.]
In order to truly see it well, we would have to graph the N’s as indicating force points in the opposite direction. Therefore, it is very interesting for us to see that the true harmonics of the tetrahedron shape appear to be a combination of very harmonic numbers and very non-harmonic numbers.
In the cases where the N’s emerge, there are very few numbers that divide into the number itself, and in the cases with many Y’s the numbers are harmonic, meaning that they have a maximum number of divisors.
Considered together, this information reveals a tremendous amount. We now have solid mathematical proof from the Enterprise Mission that connects the angles of one of the main Platonic geometries (and almost certainly the others as well) to the harmonic number series.
Furthermore, the singularly important “19.5” number, representing the most significant portion of the circumscribed tetrahedron, is the precise harmonic of the number 36, which is by far one of the most harmonic numbers of all.
In the triangle-shaped “tetracys” from Pythagoras, there are 36 rows of dots starting with one dot at the top and ending with 36 dots at the bottom. Together, this forms a triangle, and it also represents a simple system of harmonic counting.
When we summarize all the dots in the triangle together, we come to that same cornerstone ‘solar’ number, 666.
Therefore, as we look at harmonic numbers showing up in the Solar System in Part Three, we have more reason than ever to see that they can be directly connected with Platonic geometries. Even the speed of light itself appears to describe a harmonic spiral that Cathie equated with 144 in his harmonic time system based on a proportion of nine.
Before we enter into our final discussion regarding time cycles, we will finish out our look at the history of this knowledge. By examining the trickle-down effect of Atlantean knowledge into past and present “secret societies,” we can indeed trace how it was that literally all of the knowledge that we have been discussing was carefully preserved.
We will explore how it was that ancient peoples chased after these Grid energies one line at a time, through the amazing study of “ley lines” and how they emerge all over the planet. We will also explore an amazing twist to the story, by showing how a present-day secret society still exists which has never lost this knowledge.
This secret society was responsible for the formation of the United States Government, and lent its hand quite directly in the building of the United Nations Meditation Room.
We will show the amazing quality of this room, and suggest that it is indeed a hyperdimensional “machine,” built on the premises of this carefully guarded secret knowledge that is gradually becoming available to the public.


Sudoku is a logic-based, combinatorial number-placement puzzle that’s a lot more fun than it sounds.
The goal is to fill a 9×9 grid with numbers, with each row and column containing the numbers 1 to 9. Sudoku’s difficulty level can be adapted making it a fantastic game for all levels and ages of play!
Sudoku is a relatively new game considering its popularity. The modern version of Suduko was first published in 1979. Now, there are Sudokos in every paper and hundreds of Sudoku-inspired board games to choose from.
Even if you’re not a massive Sudoku player, playing it can help improve your concentration, problem-solving skills, and improve your memory. All skills needed to triumph in the real world (and the world of board games).
If you’re a fan of Sudoku or looking to get into the game, you’ll love our list of the best Sudoku board games!
🏆 Our Top Picks for Best Sudoku Board Games
In a hurry? Take a quick peek before you go.
Best Sudoku Board Games
We hope you enjoyed our list of the best Sudoku board games! This classic number puzzle is a great way to challenge yourself, keep your mind sharp, and kill some time between other activities. Sudoku is mentally stimulating and addictive, so play these Sudoku board games at your own risk!
Have you tried playing any of these versions of Sudoku board games? Drop a comment below and let us know what you think! We’d love to hear from you.
You may also enjoy:
Looking for more brain teaser board games? Check out our best word games below:
Kendra has always been a hardcore fantasy nerd. Growing up in the worlds of Tolkien, Sanderson, Jordan, and Abercrombie, DnD & board games just came naturally. She and her husband, Bryan, started GameCows.com in 2018 as a fun passion project that just took over their lives. An avid board gamer since childhood and chronic DnD chronicler for more than two decades, she loves to play, write, travel, and learn dead languages.


Whether I'm ready or not, racing season seems to have already started. I've already paid for two races, the Yukon Days 3 mile Snowshoe Race and tomorrow's Securian Half Marathon, where Laura will be running her first race of the year. I'm now debating whether or not to sign up for the Afton Trail Run 50k in July, and then the Chicago Marathon in October.
I guess tomorrow's half marathon is not really a "race" for me, as my training has been pretty miserable up to this point. If I want to run the Afton 50k, I'm really going to have to stay on top of keeping up with injury prevention and start running a little more consistently.
I want to train for a 50k again for two main reasons. First of all, I really enjoyed my last Afton 50k. Secondly, I love telling people I'm training for a 50k so they get all impressed and say something like, "that's so far." Plus, it's great when people ask, "how far is 50k?"
I like to think that I'm not some running snob who thinks that anyone who has to ask, "how far is a 5k?" or, "how far is your marathon?" is a total moron. I am, however, a little bit of a math snob. So when a runner or someone who I know has run multiple 5ks asks me how far a 50k is, I have a really hard time not saying, "try multiplying 3.1 miles by 10, genius."
I have such a hard time not saying that or something like it, that sometimes I do mistakenly let my math snobbery slip and say, in a real sarcastic manner, "well, a 5k is 3.1 miles and a 50k is ten times farther than that." It feels mean, but sometimes I just can't help it. It amazes me how many people make it through life without being able to multiply by ten. Of course, if we just went with the international system of measurement and measured everything by kilometers and all those other great metric measurements, none of this would be a problem.
Tomorrow the Securian Half Marathon may be cut to a quarter marathon due to horribly cold weather. A quarter marathon is half of a half marathon, and a half marathon is 21k. Since I've learned from experience that most people have no interest in doing the math to figure it out, a quarter marathon is 10.5 kilometers, or 6.55 miles. I guess I'll find out tomorrow morning if I'll be running 13.1 miles in bone-chilling wind chills of -17 degrees Fahrenheit, or only 6.55 miles in internal organ-freezing wind chills of -20 degrees Fahrenheit.


Yr 5 – Mrs Croydon & Mr Biggs – Kinder Scout
Our Topic this term is Groovy Greeks. Please encourage your child to investigate our history topic. Homework for this term is shown below and will be shared with the class weekly.
Weekly spellings focus on high frequency words as listed in the National Curriculum. Children will continue investigating and learning the year 5 and 6 words. Spellings will be given on a Monday and tested the following Monday. The spellings to be learned will be highlighted in their diary and then the children will √ the ones they spelled accurately.
Please continue to encourage your child to read at home. In their diary are a list of other activities which will develop your child’s love of reading and the reading experience, try to complete at least 4 of them weekly. We always welcome book reviews and recommendations to encourage other readers in class, book review sheets are available in class. When completed come and display the review for other children to read.
This will be given out on Friday to be completed and returned any day but by the following Friday at the latest. Please encourage your child to complete this homework as it supports the grammar, punctuation and spelling learning, which takes place within the classroom. Your child will complete this task independently weekly.
In Numeracy this term we will be concentrating on multiplication and division, fractions and geometry.
A quick recall of times tables facts are an essential skill to support understanding in mathematics. Encourage your child to practise, as all children in year 5 need to know their times tables to 12 x 12 and the related division facts. Times Table activities are completed weekly.
Maths Skills Check
Homework will be given weekly to support and consolidate the learning in class. This is given out on Friday to be completed and returned any day but by the following Friday at the latest. Your child should use the ‘Prompt Sheets’ to support them. They will complete this task independently.
PE will be on Thursday and Friday afternoons. Please ensure that your child has both an indoor and outdoor PE kit on these days, as we will be venturing outside as much as we can.
FOR YOUR CONTINUED SUPPORT
Times tables – A quick recall of times tables facts are an essential skill to support understanding in mathematics.
School closes for the Summer on 20.07.2018 and re-opens on Tuesday 4th September 2018.
14/07/2018 - Hady Primary School is 50 this year and to celebrate we are holding a Celebration Fun Day on 14th July from 2.00pm to 7pm come and join us for a great afternoon of fun and activities.


D.M. Pan Real Estate Company
Median Housing Price Prediction Model for D.M. Pan Real Estate Company
Recall that samples are used to generate a statistic, which businesses use to estimate the population parameter. You have learned how to take samples from populations and use them to produce statistics. For two quantitative variables, businesses can use scatterplots and the correlation coefficient to explore a potential linear relationship. Furthermore, they can quantify the relationship in a regression equation.
This assignment picks up where the Module Two assignment left off and will use components of that assignment as a foundation.
You have submitted your initial analysis to the sales team at D.M. Pan Real Estate Company. You will continue your analysis of the provided Real Estate County Data spreadsheet using the Mountain Region to complete your analysis. You may refer back to the initial report you developed in the Module Two Assignment Template to continue the work. This document and the National Statistics and Graphs spreadsheet will support your work on the assignment.
Note: In the report you prepare for the sales team, the dependent, or response, variable (y) should be the median listing price and the independent, or predictor, variable (x) should be the median square feet.
Using the Module Three Assignment Template, specifically address the following:
• Regression Equation: Provide the regression equation for the line of best fit using the scatterplot from the Module Two assignment.
• Determine r: Determine r and what it means. (What is the relationship between the variables?)
Determine the strength of the correlation (weak, moderate, or strong).
Discuss how you determine the direction of the association between the two variables.
Is there a positive or negative association?
What do you see as the direction of the correlation?
• Examine the Slope and Intercepts: Examine the slope b1b1 and intercept b0b0.
Draw conclusions from the slope and intercept in the context of this problem.
Does the intercept make sense based on your observation of the line of best fit?
Determine the value of the land only.
Note: You can assume, when the square footage of the house is zero, that the price is the value of just the land. This happens when x=0, which is the y-intercept.
• Determine the R-squared Coefficient: Determine the R-squared value.
Discuss what R-squared means in the context of this analysis.
• Conclusions: Reflect on the Relationship: Reflect on the relationship between square feet and sales price by answering the following questions:
Is the square footage for homes in your selected region different than for homes overall in the United States?
For every 100 square feet, how much does the price go up (i.e., can you use slope to help identify price changes)?
Use the regression equation to estimate how much you would list your house for if it was 1,200 square feet.
What square footage range would the graph be best used for?
Guidelines for Submission
Submit your completed Module Three Assignment Template as a Word document that includes your response and supporting charts/graphs.


Not so long ago, I read an article on fibonacci. I suggested a more elegant solution to my eyes, but the problem kept bogging me. Let's get into it!
The first implementation, which reads like the mathematical formula, looks like this:
def fib(0), do: 1 def fib(1), do: 1 def fib(n), do: fib(n-1) + fib(n-2)
The main issue with this implementation is that the bigger the index you calculate, the exponentially bigger is number of operation needed. To show how, let's look at the following graph of calls of the
As you can see
fib(2) is calculated 3 times, which is a inefficient. The number of recursive calls of
fib will grow exponentially as we advance in the sequence. My computer start having big problems when attempting to calculate
fib(35). You could even get the result before you computer, which is a pretty bad sign! Let's find another way to remove most of that calculation.
Memoization is an optimisation technique that speeds up algorithm by saving intermediate function calls which are used multiple times. In our case, if we calculate
fib(n), we'll save every
i < n.
Although this technique will yield much better results at a benchmark, it is not yet an optimized version of the algorithm.
The last algorithm optimization available is called dynamic programming. It seems like a complex word, and it covers a lot of techniques but in the case of Fibonacci, the algorithm is elegant and intuitive.
The first thing you have to ask yourself is: "How would I calculate
fib(5)?" Let's try to make it step by step:
fib(2) = fib(1) + fib(0) = 1 + 1 = 2 fib(3) = fib(2) + fib(1) = 2 + 1 = 3 fib(4) = fib(3) + fib(2) = 3 + 2 = 5 fib(5) = fib(4) + fib(3) = 5 + 3 = 8
For each step you only used 3 explicit variables,
fib(i - 1),
fib(i - 2) and an implicite one, the sequence number we calculate
n (5 in this case). It's pretty simple to implement a function which will replicate this behavior:
def fib(0), do: 1 def fib(1), do: 1 def fib(n), do: dyna_fib(1, 1, n) def fib_step(result, _, 1), do: result def fib_step(fib_i_minus_one, fib_i_minus_two, i) do fib_step(fib_i_minus_one + fib_i_minus_two, last, i - 1) end
It's a very fast implementation, it's complexity drops to
O(n). This version calculates very easily the millionth element of the Fibonacci sequence!
As you might know, the Fibonacci sequence is a mathematical object. Maybe maths have some interesting formulas, you can find the most interesting formula in the end of this chapter
Fib(2n - 1) = F(n)² + F(n - 1)²
Fib(2n) = (2 * F(n - 1) + F(n)) * F(n)
Those formulas are a huge improvement! They would allow to jump indices of the sequence by a factor of 2! This will allow to reduce the complexity to
O(log(n)), which is quite impressive. The implementation is straight forward:
def log_fib(0), do: 0 def log_fib(1), do: 1 def log_fib(2), do: 1 def log_fib(n) when rem(n, 2) == 1 do # Fib(2n - 1) = F(n)² + F(n - 1)² i = div((n + 1), 2) first = log_fib(i) second = log_fib(i - 1) first * first + second * second end def log_fib(n) when rem(n, 2) == 0 do # Fib(2n) = (2 * F(n - 1) + F(n)) * F(n) i = div(n, 2) first = log_fib(i) (2 * log_fib(i - 1) + first) * first end
Instead of getting all the problems with implementing an optimized version, you should use a library that does the job for you. Gnu MP is, as far as I know, the most optimized version of Fibonacci and uses a memoized version of the
O(log(n)) recursive algorithm.
I didn't think I would get so deep when starting the article. I wanted to show off with dynamic programming, but in this case it's not even the optimized version. The lesson of this article should be: always doubt on an opinion you have on a subject you don't know well. We tend to take our opinions for truth, but if we confront them to a methodological and rigorous research process, they always prove to be, at best, misleading.


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1. Implement the DFS to check experimentally the theoretical result for the
Poisson random graph with mean degree z = p(n − 1).
- The fraction S of vertices in the giant component is the largest solution ofS = 1 − exp(−zS);
- Let v be a randomly chosen vertex from a non-giant component. The averagesize of the component to which v belongs is11 − z + zSProceed as follows. Program the DFS (from scratch). Set the number of vertices n = 1000. Define a grid of values of z ranging between 0 and 4. For each z, generate r = 100 random graphs G(n, p) where p = z/(n − 1). For each graph, use the DFS to find its connected components. Calculate ⟨s(z)⟩ and S(z). Make two figures:
- Figure 1: find numerically and plot the theoretical values S(z) versus z. Also plot the experimentally found values for S(z).
- Figure 2: plot the theoretical value for ⟨s(z)⟩ = [1 − z + zS(z)]1 and the exper- imentally found values for ⟨s(z)⟩.Comment on your findings. Link files with your codes to the pdf file with your report.2. (5 pts) Implement the BFS to obtain estimates for the average length of shortest paths in the Poisson random graph:log(n)l≃ . (1)log(z)Proceed as follows. Program the BFS (from scratch). Set z = 4 so that almost all vertices belong to the giant component. For n = 2p, p = 10, 11, 12, 13, generate a random graph G(n, p). Randomly select r = 100 vertices, and use each of them as a seed for the BFS. Average the found path lengths and find l(n). Plot the found l(n) versus n as well as the theoretical estimate (1). Comment on your observations. Link files with your codes to the pdf file with your report.3. (5 pts) Read Sections II.A, II.C, and II.D in Newman, Strogats, Watts, Random graphs with arbitrary degree distributions and their applications, Phys. Rev. E, 64, 026118. Consider a random graph with a prescribed degree distribution pk. Let v be a randomly chosen vertex from a non-giant component. Write a book report with a detailed derivation of the formula for the average size of the component to which v belongs to:
⟨s⟩ = 1
zu2[1 − S][1 − G1(u)]


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IIT JEE Super Course in Mathematics: Calculus written by Trishna Knowledge Systems .
IIT JEE Super Course in Mathematics: Calculus is a class-tested course content package for sure-shot success at the IIT-JEE. Each volume in this series is meticulously planned and structured to help the user imbibe and absorb concepts and apply them to IIT problems. This title follows a unique, user-friendly approach, with features such as Concept Strands, Concept Connectors, Topic Grip, IIT Assignment Exercise, which make the learning and application for the coveted IIT-JEE circuit both easy and enjoyable.
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Title: IIT JEE Super Course in Mathematics: Calculus
Author(s): Trishna Knowledge Systems
Publisher: Pearson India
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Fundamental problems in dynamic meteorology; components of the equations of atmospheric motion are derived, and vorticity and divergence in the development of meteorological systems. Prereq: 5950 (631), and Math 2153. Not open to students with credit for 637.
Credit Hours: 3.0
Syllabus SP18-ASP 5951-Liu,Z.pdf
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One of my favourite lessons that I have done with my students was a maths lesson focusing on counting. As a warm up, the students and I sang along to two counting videos on the interactive whiteboard (IWB) firstly we counted from 1 – 20 and then we counted backwards from 20 – 1. After this I introduced the students to a pirate counting warm up where they had to count a certain numbers of objects in the image e.g. How many pirates are on the ship? Then, I divided the students into 4 teams and introduced them to an online pirate board game where students had to click on the dice to roll it, watch the pirate ship move and answer a math question when the pirate ship stopped on a space. I incorporated this online board game with Pop Up Pirate, a game where swords are pushed into the pirates barrel until the pirate pops out of the barrel. When students answered a question correctly on the IWB game they got to put a sword in the barrel, if they made the pirate pop they got to collect a gold pirate coin for their team!
The kids loved this game and it was a great way to incorporate the IWB into a whole class counting activity!


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Free Kindergarten math worksheets for children to supplement their math activities at home or in school. Each math worksheet has an answer sheet attached on. 1 5. 4 0. 8 3. 2 6. 8 3. 9 1. 0 7. 8 9. 10 8. 7 5. 5 6. 1. 2. 3. 4. 5. 6. 7. 8. 9. Math Worksheet. Name__________________________________. Date. Math Worksheets For Pre Kindergarten or Preschool On: Addition, Numbers, Shapes, Spelling numbers, Tracing shapes and more.
They will begin to realize that patterns also occur in real life. They will be doing activities like; telling the time , how to use a calendar, how to measure quantities, using different patterns and to predict about what comes next.
Kindergarteners should also do physical math.
This is great for them as they will use it for the rest of their lives. They will be able to find and know the value of up to 20 coins. They will be able to identify the different coins and currencies.
They should know the names of the measurement devices, like; a ruler, a scale, a thermometer, clocks, calendars and measuring cups and spoons. They should know the different measurement terms, like; length, weight, temperature, time and volume. It is important that they know the different geometric shapes circle, square, rectangle and the triangle , for it will be used the rest of their lives. They will be able to sort items into different groups, like; colour, shape, size and material.
The children will be expected to learn important numbers, like; the telephone number, the emergency number, different birthday dates and their street address. Some great activities that parents or teachers can do with their children or their class are; playing the blue bean game, where your child can learn to count little blue beans. Let the children make and cut out all the numbers that they know about, and then let them make up their own sums.
These addition worksheets are free for personal or classroom use. Addition Worksheets Subtraction Worksheets This is the main page for the subtraction worksheets. Follow the links for Spaceship Math Subtraction worksheets, timed subtraction tests, multiple digit subtraction worksheets, simple borrowing and regrouping worksheets, and math worksheets with mixed addition and subtraction problems Subtraction Worksheets Multiplication Worksheets This is the main page for the multiplication worksheets.
Put your fingers away, because this is the first math operation where memorization of the facts is a requirement. You'll find multiplication worksheets for Dad's Eight Simple Rules for Mastering the Times Table, RocketMath Multiplication, multiple digit multiplication, squares and other multiplication worksheet topics.
All of these multiplication worksheets include answer keys and are instantly printable and ready classroom or home school use. Multiplication Worksheets Division Worksheets This is the main page for the division worksheets.
This includes Spaceship Math Division worksheets, multiple digit division worksheets, square root worksheets, cube roots, mixed multiplication and division worksheets. These division worksheets are free for personal or classroom use.
Division Worksheets Multiplication Chart Trying to memorize the multiplication facts? This page contains printable multiplication charts that are perfect as a reference.
There are different variations of each multiplication chart with facts from products , products , products and products Each of these multiplication charts is a high resolution SVG, so the multiplication facts print beautifully!
Multiplication Chart Multiplication Table Are you looking for a printable multiplication table that has more than just the facts?
One with some extra math facts about the multipliers? Or a unique design? In color? The multiplication tables on this page are all high resolution SVG files that print beautifully on your printer and are great resources for learning the times tables in the grade school classroom or at home!
Multiplication Table Fact Family Worksheets Fact family worksheets focus on sets of related math facts, not specific operations.


Creative learning center
Creative learning center with nice development elements
The Creative Learning Center is very nice for the little kids. The Learning Center has a variety of fun learning elements such as a snake with the alphabet and a shoe lace where children can learn to tie their shoes. Furthermore, they can do the math on the math square, play with different shapes and play x’s and o’s. Moreover, there are nice play elements so that the children can climb and slide.
The learning center is designed in the popular colors red, yellow, blue and green. The learning center is easy to set up and the kids will have hours of fun from it.
Customize your inflatable game!
Furthermore, this game can be made in any color and with any desired logo. Pimp your game with your own personal customized design. Ask for the possibilities and contact us now!
Thanks to our excellent quality will last your inflatable years.
|Dimensions :||6,0 x 6,0 x 1,6 (L x W x H)|
|Packed size :||0,9 x 1,1 M|
|Weight :||77 kg|
|Weight blower :||15 kg|
|Set up time :||10 minutes|
|Install, pack up :||1-2 persons|
|Capacity :||8 persons|
- Blower 1,1 kW
- Stakes (6 pieces)
- Repair kit
- Transporting bag
- Safety certificate EN 14960
- 5 year warranty
- 5 year of free repair service


In mathematics, the chord of a circle is a segment that connects two points on a circle. A chord that passes through the centre of the circle measures its diameter. On an airplane, the chord also measures a distance between two points at a specific location on the aircraft. When it varies, as is the case on some ‘planes, an average, called the "mean aerodynamic chord", is calculated.
But what exactly does the chord on a ‘plane measure? Look for the answer at the end of the video, in which we let several passengers express their opinion.


Caring Campus Coach
Dr. Jovanovich has worked with 23 colleges in 12 different states as a data coach for Achieving the Dream. She is a consultant with the Dana Center in their math pathways work and teaches educational research methods for the John Roueche Community College Leadership Program at Kansas State University.
Retired from John Tyler Community College in Richmond, Virginia, Dr. Jovanovich coordinated strategic planning, assessment, program evaluation, research and reporting. Prior to coming to John Tyler, she served as the Director for Institutional Effectiveness at the Virginia Community College System Office, where she did state‐level policy work with Achieving the Dream, worked with the Community College Research Center, and served on the Achieving the Dream Cross-State Data Work Group.
Dr. Jovanovich’s extensive experience with community colleges as an administrator and a mathematics professor includes the conduction of numerous studies of student success in the workforce, distance education, and college readiness.
Having begun her community college career teaching mathematics at J. Sargeant Reynolds Community College, she also served as assessment coordinator, prepared college‐wide assessment reports on student learning outcomes, developed a model for program evaluation and directed the self‐study for reaffirmation of accreditation. At Virginia Commonwealth University, she developed a mechanism for comprehensive reporting to document “completing the loop” of institutional effectiveness through a useful and usable web‐interface tool.
Dr. Jovanovich holds a Ph.D. in education, with a concentration in research and evaluation, from Virginia Commonwealth University; an M.S.T. in mathematics from the University of Wisconsin‐Oshkosh; and a B.A. in mathematics from Lake Forest College.
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On 1 March 2011 population of Latvia was 2 070 371
Population of Latvia on 1 March 2011 in accordance with the 2011 Population and Housing Census data was 2 070 371.
Since the previous Population and Housing Census 2000 the population has decreased by 307 thousand population or by 13 %.
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