2.5: Lab 5 - More about Folds - Geosciences

2.5: Lab 5 - More about Folds - Geosciences

Multiple planes on the stereographic projection

The techniques you used in the last lab work well for folds that are perfectly cylindrical, and where the orientations of the folded surfaces are known with great precision. Under these circumstances, to determine the orientation of a mean fold axis, it is desirable to measure a large number of orientations, and to use a statistical approach.

Unfortunately, plotting large numbers of great circles rapidly produces a very cluttered projection. For this reason, it is much better to plot poles to the folded surfaces rather than great circles. In the ideal case the poles should all lie in the profile plane, and therefore they will plot as points on a single great circle. In real life, things are not so simple; the poles appear scattered in a band, or girdle, on either side of the profile plane, which has to be estimated as a ‘best-fit’ great circle through the densest band of points.

There is an additional problem, however. If you look at the Wulff net, you will see that the 2° and 10° squares project much larger near the primitive than they do at the centre of the net. This means that plots made with the Wulff net should never be used for statistical inferences based on density of points, because it artifically increases the density in the centre and decreases it on the primitive.

For this reason, a modified stereographic projection, called the equal area projection is used, based on the Schmidt net. All the operations you have met so far are the same on the two nets; the only difference is that the equal area projection does not preserve circular arcs – the great and small circles are complex curves and cannot be drawn with a compass. For this course make sure your net is printed so that its diameter is exactly 15 cm.

Pi diagram

The resulting plot of poles to planes on a equal area projection is called the pi-diagram, which is the most common method used to find the mean fold axis in an area of folded rocks where, as often happens, individual fold hinges are not exposed. The principle of the pi-diagram is illustrated in Figure 1. In a cylindrical fold, the poles to the folded layers are lines perpendicular to the fold axis. They therefore lie in the profile plane, the plane that is perpendicular to the fold axis. If the folds are not perfectly cylindrical, or if there are small errors in the measurements, the lines will not lie precisely in the profile plane, but will be close to it.

Contours on the axial surface

Maps of areas with folded rocks can be challenging because of the number of surfaces involved, and because of rapid changes of strike and dip. Often, even though layers may show complex folding, axial surfaces may be approximately planar. Under these circumstances it makes sense to separate the limbs of the fold by drawing axial traces, and even to draw contours on the fold axial surfaces. When doing this, it’s important to remember that a single fold will have multiple hinges (one for each folded surface), but that these hinges lie in a single fold axial surface.


1.* The area you contoured last week (Great Cavern petroleum prospect) shows strike and dip symbols representing measurements of bedding orientation.

Plot poles to bedding for all the strike and dip measurements on an equal area projection, to make a pi-diagram. Find and draw the best-fit great circle through the poles; this represents the profile plane. Mark the best estimate of the fold axis (pole to the profile plane) and determine its trend and plunge. Is it similar to the value you obtained by contouring last week, and to the values obtained by your other team members?

2.* Look at the map of Somerset County in the Appalachians of Pennsylvania. The area has a long history of coal mining, and a number of coal seams are identified on the stratigraphic column that doubles as a legend.

a) The map has structure contours, shown in red, drawn on one surface. Which one surface? (Note: each formation on the map has a top and a bottom surface, so just a formation name is not a complete answer; your answer should be in the form ‘the boundary between Formation x and Formation y’.)

b) Use the spacing of the structure contours to determine the strike and dip, at its steepest point, on each limb of the most conspicuous fold. Note that the contours are in feet, and the scale of the map is 1:62500 (about 1 inch to 1 mile). Make sure that in your dip calculation you use the same units vertically and horizontally. Use the points where the contours cross the fold hinge to determine the average trend and plunge of the fold hinge.

c) Plot both limbs of the fold from part ‘b’ on a stereographic projection. Using the intersection and the angle between the planes, estimate the plunge and trend of the fold axis, and the interlimb angle of the fold.

d) Based on these observations, describe the orientation (plunge, tightness, overall orientation) of the fold in words (e.g. ‘tight, steeply plunging synformal anticline’)

e) If the fold is cylindrical, the fold axis orientation determined stereographically should coincide with the hinge orientation determined by contours. How close are they (in degrees)?

3. Map 1 contains an angular fold in a more general orientation than the perfectly horizontal folds you dealt with last week. In addition there are some unfolded rocks and an intrusion. An unconformity separates the more highly deformed folded rocks from the gently dipping younger rocks. To help you solve the map, note that in the west of the map, the bedding traces are somewhat parallel to the topographic contours. These regions correspond to a gentle fold limb. Elsewhere, the geological boundaries cut across the contours at a steeper angle; this is a steep fold limb. Fold hinges can also be identified on the map from sharp swings in the trace of bedding that are not obviously related to valleys and ridges. Before you begin, try to use these hinges to sketch where there might be fold axial traces; these should separate regions of steeper and more gently dipping beds. Do this very lightly – it is likely you will change your mind as you proceed.

a) Identify the various surfaces on the map. First, mark the unconformity surface in green or yellow. Then mark the boundary between marble and amphibolite in blue or violet. Mark the boundary between amphibolite and schist in red or orange. (Note: the colour scheme is provided for convenience. If you choose different colours, you must use them consistently throughout this exercise.)

b) Draw structure contours on the green surface.

c) Draw structure contours on the red surface. You will find that there are two parts to this surface: a steep limb and a gentle limb. These have separate sets of contours. The two sets of red contours intersect in a fold hinge. Mark this on the map and trace over it with red.

d) Repeat for the blue surface and mark the blue hinge.

e) The red hinge and the blue hinge are both lines that lie in the axial surface of the fold. Join points of equivalent elevation on the red hinge and blue hinge with lines: these are structure contours on the axial surface. Number them in purple or violet.

f) Use the axial trace contours to predict the outcrop trace of the axial surface, and draw this trace on the map. The axial trace should separate the steep limb from the gentle limb of the fold.

g) Make a cross section along the line XY.

h) Plot both fold limbs, the axial surface, and the unconformity as great circles on an equal area projection. Mark the point corresponding to the orientation of the fold axis.

i) Describe the orientation of the fold in words as completely as you can

j) List the events in the geological history of the area for which you have evidence, starting with the oldest. In the case of the three folded units, where there is no direct evidence of age, you should assume that the fold is upward facing (i.e. synforms are also synclines; antiforms are also anticlines).

2.5: Lab 5 - More about Folds - Geosciences

The Exploratorium is more than a museum. Explore our online resources for learning at home.

  • 4 to 6 books (enough to make 2 stacks the same height)
  • A package of file cards
  • 300 to 400 pennies (loose or in rolls)
  • Scissors

Make 2 stacks of books with a gap of about 4 inches between them. Make sure the stacks are the same height.

Lay one file card over the gap between the books. About 1/2 inch of the card should be resting on a book at each end. How many pennies do you think you can pile on this flat bridge before it falls into the gap-5? 10? 100? Try it and see how close your guess was.

As an advertising stunt for a paper company, Lev Zetlin Associates designed a full-sized paper bridge that was strong enough to support a car!

Without adding anything to the file card, try to make your bridge stronger. How could you change a file card to make it stiffer? What happens if you fold the card in half? If you make an arch? How about if you fold the card into pleats?

Make a bridge, then test it to see how many pennies it will hold. Some of your bridges may hold a few pennies before falling down. Others may be stronger, but the pennies may slide right off. And some bridges will probably hold a lot more pennies than you'd think.

How many pennies can my file-card bridge hold?
You may find that a file-card bridge can hold more pennies than you'd think! Here are the results of the file-card bridges that the Science-at-Home Team built.

A roll of 50 pennies weighs 132 grams-that's a little more than 41/2 ounces.

How many kinds of bridges are there?
You might think that bridges come in an infinite variety of forms. But if you get right down to the structural elements of a bridge, there are really only three kinds: beam spans, arch spans, and suspension spans.

The simplest kind of bridge is a beam bridge. A log that has fallen across a river makes a beam bridge. So does a board laid across a puddle, or a span of steel laid across a body of water, or a file card laid across two books. A beam bridge relies on the stiffness of the building material. If the log across the river sags, it doesn't make a very good bridge.

Arches have been common features in buildings since 1,000 B.C., but they didn't appear in bridges for another thousand years. Roman roads, built at the height of the Roman Empire's power, were often supported by stone arches.

Suspension bridges, like the Golden Gate Bridge in San Francisco, rely on a cable or rope for their support. Each end of the cable or rope must be anchored to the bank-tied to a tree, a boulder, or (in modern suspension bridges) a massive block of concrete called an anchorage. The cable or rope pulls on the anchors, but as long as they don't move and the cable or rope doesn't snap, the bridge is stable.

What kinds of bridges can I make with my file cards?
Using just your file card, you can make two of the three different kinds of bridges. When you lay a file card across two books-even if you've folded the card into pleats first-you've made a simple beam bridge. If you cut slots into the card, tuck the flaps under the edges of the book covers, and push the books slightly together, you'll make an arch bridge. We haven't figured out how to make a suspension bridge out of a file card, though. If you come up with a way to do it, please let us know!

This and dozens of other cool activities are included in the Exploratorium's Science Explorer books, available for purchase from our online store.

Published by Owl Books,
Henry Holt & Company, New York,
1996 & 1997

Caudal regression syndrome is a complex condition that may have different causes in different people. The condition is likely caused by the interaction of multiple genetic and environmental factors. One risk factor for the development of caudal regression syndrome is the presence of diabetes in the mother. It is thought that increased blood sugar levels and other metabolic problems related to diabetes may have a harmful effect on a developing fetus, increasing the likelihood of developing caudal regression syndrome. The risks to the fetus are further increased if the mother's diabetes is poorly managed. Caudal regression syndrome also occurs in infants of non-diabetic mothers, so researchers are trying to identify other factors that contribute to the development of this complex disorder.

Some researchers believe that a disruption of fetal development around day 28 of pregnancy causes caudal regression syndrome. The developmental problem is thought to affect the middle layer of embryonic tissue known as the mesoderm. Disruption of normal mesoderm development impairs normal formation of parts of the skeleton, gastrointestinal system, and genitourinary system.

Other researchers think that caudal regression syndrome results from the presence of an abnormal artery in the abdomen, which diverts blood flow away from the lower areas of the developing fetus. Decreased blood flow to these areas is thought to interfere with their development and result in the signs and symptoms of caudal regression syndrome.

Some scientists believe that the abnormal development of the mesoderm causes the reduction of blood flow, while other scientists believe that the reduction in blood flow causes the abnormal mesoderm development. Many scientists think that the cause of caudal regression syndrome is a combination of abnormal mesoderm development and decreased blood flow to the caudal areas of the fetus.

Origami inspired 2: more pleats and folds using ribber

Periodically I search out previous drafts, this post was started in September 2019. Drawn to folds in a variety of ways again, I am publishing it in progress with the intent of adding more and information and related swatches.

Some previous posts with related topics and technique swatches: origami-inspired pleats1, racked patterns Passap/Brother 2, ribber pleated fabrics, and some possible needle arrangements 3.
There are many considerations if long panels or wide ones are required when setting up repeats in addition to what happens at the edges of patterns in racking as one bed moves near or past the needles in work on the opposite bed. If something like a skirt is planned, the choice must be made as to which side of the knit is preferred, and the end stitches of each panel should be on the underside of the piece unless the join is a deliberate design feature. To achieve that, some panels may need to be wider than others. If the pleats are bulky and involve deep foldovers, panels may be attached to yokes to reduce bulk at the hips. If working from illustrations for pleats for another brand, the needle setups shown may need to be reversed, or, since many such fabrics are reversible, if manual set up and no additional patterning on the Japanese machines knit bed or European true double bed they can be knit as illustrated. Lock settings for the Passap are given with the back lock first (ribber settings on Brother), then for the front bed lock (top, knit bed on Brother). Cast ons must be fairly tight so there is no flare at the bottom of the pleats. They usually start on a standard needle setting. Needle transfers are usually made after the cast-on is completed, sealing the stitches with one row of all knit stitches. Swatches should be a minimum of 100 stitches wide by 100 rows if the end goal is a gauge significant garment. All fabrics with texture may change in both appearance and gauge after a period of rest. Some shaping if needed may be obtained by tension changes, OOW needle arrangements on either or both beds, or stitch type within folds (ie adding fisherman, half fisherman, EON patterning, etc.)
Pleat formation on the double bed is “easy” because the pleats are formed “automatically” according to the needle arrangement on each bed. That is true if the resulting folds are created by stocking stitches in vertical bands. My goal is not to provide patterns. There are many well-written ones easily available.

How small can one go? A tiny pleat: It is easier to transfer stitches when the ribber is set to P (Passap handle up). Remember to return the setting to half-pitch before continuing. The pleat is reversible, shown on both sides, reminds me of shadow pleats racking by one position X3 at first, and then X 5 in each direction did not produce results worth the effort IMO, the result is subtle, the reverse side of the fabric is slightly stretched in the bottom photo. Here the fold is created by 2 stitches tucking for 2 consecutive, then knitting on the same needles for 2 rows on regularly spaced pairs of needles on either bed. Most knitting is on a single bed. A lacey series of eyelets begin to appear, and in some random racking at the top of the swatch, the possibility of developing a secondary pattern due to the combination of racking and tucking begins to show. The middle image is of the fabric slightly stretched. Passap Brother: the ribber can do the stocking stitch background, every needle in work, carriage set to knit. The setup is the same as the Passap diagram. A repeat with 2 black rows of squares followed by 2 white can be programmed on the top bed. On every needle selected rows, pairs of needles will knit, on the white, no selection rows the same pairs of needles will tuck for 2 rows. Moving away from vertical ribs becomes significantly easier if one has a G carriage. The alternative option is to create geometric folds that require transferring between beds. Any of these fabrics are best knit in a yarn that has memory and can spring back. Yarns such as acrylic can be permanently flattened by pressing, resulting in loss of texture. A quick experiment: black cells represent knit stitches, blue purl ones The needle setups: after casting on, transfer for a stitch configuration based in this case, of blocks that are 5 stitches wide. A single needle on the opposite bed is used on each outside edge of all needles in work. When there are no groups of stitches in work on both beds the pitch can be set to and remain on P, which also will make transfers easier, as needles will be point-to-point. The ratio used in the test was in multiples of 5. The groups were 5 stitches wide, 15 rows high, with all knit 10 rows in between the repeats. The fabric is shown first relaxed as immediately off the machine, then lightly steamed and stretched. The yarn is a 2/18 wool, far too thin for this use, and likely to flatten considerably with pressing. The close-up of the purl side offers a better view of the resulting folds The repeat, 10 stitches by 40 rows. More on Knit and purl blocks to create folding fabric_ “pleats”Pleated, plaited shadow lace Pleated one color “shadow lace” in Slip stitch patterns with hand transferred stitches, double bed

Pleated dbj A repeat that will spiral, usable in spiral socks Spaces between any and all blocks may be adjusted to suit one’s preferences.

2.5: Lab 5 - More about Folds - Geosciences

CHAPTER 10: Folds, Faults and Rock Deformation

1. Figure 10.6 : Rocks that were originally deposited in horizontal layers can subsequently deform by tectonic forces into folds and faults. Folds constitute the twists and bends in rocks. Faults are planes of detachment resulting when rocks on either side of the displacement slip past one another.

How Rocks Become Deformed

Three Types of Tectonic Forces

1. Figure 10.6: There are basically 3 types of tectonic forces that can deform rocks. The type of strain (deformation) that develops in a rock depends on the tectonic force.

(a) Compressive forces squeeze and shorten a body.

(b) Tensional forces stretch a body and pulls it apart

(c) Shearing forces push different parts of a body in opposite directions

2. The type of deformation experienced by a rock body depends largely on the type of force exerted.

(a) Fig. 10.6a: Compressive forces generate folding and faulting as a consequence of shortening. Compressive forces are common along convergent plate boundaries resulting in mountain ranges.

(b) Fig. 10.6b : Tensional forces cause stretching and thinning of the rocks, usually accompanied by tensional faults. Tensional forces common along extensional plate boundaries such as mid-ocean ridges.

(c) Fig. 10.6c : Shearing forces cause rocks to slide horizontally past one another such as along transform plate boundaries to produce extensive fault systems.

What Determines Whether a Rock Bends or Breaks?

1. Figure 10.7 : Another factor that determines how a rock deforms is confining pressure , which is like the pressure you feel when you dive deep underwater. Under confining pressure, forces push against a body in all directions. In effect, the body is squeezed into itself.

2. Confining pressures within the earth are caused by the weight of the overlying rock pushing downward and from all sides. Drillers experience great problems with confining pressure. Holes drilled within the earth’s crust tend to remain open at shallow depths, but at greater depths holes tend to squeeze shut due to the increase in confining pressure.

3. Fig. 10.7b : When an external force is applied to buried rocks under low confining pressure, such as near the surface of the earth, the rock typically deform by simple fracturing. This is known as brittle deformation.

4. Fig. 10.7c : At higher confining pressures, a similarly directed external force will cause the deeply buried rock to actually flow and deform without fracturing. This is known as ductile deformation and the rock is said to behave plastically .

5. Rocks under low confining pressures near the earth’s surface therefore generally deform through fracturing and faulting. Rocks deep within the crust under high confining pressures deform by folding.

Brittleness and Ductility

1. Figure 10.7 : Rocks are defined as brittle or ductile on the basis of the way they are deformed by forces.

2. In brittle deformation, a continuous, force is applied to a rock. As the force is gradually increased, little change occurs in the rock until suddenly it fractures.

3. In ductile deformation, a gradually increasing force will cause the rock to undergo smooth and continuous plastic deformation. The rock will contort and change shape without fracturing.

4. The type of rock also determines the type of deformation. Under similar confining pressures, halite (rock salt) is more susceptible to ductile deformation than is granite, which will more likely fracture.

5. Igneous and metamorphic rocks tend to be stronger and thus resist deformation to a greater extent than sedimentary rocks.

1. Figure 10.4 : The orientations of rock layers, folds, fractures and faults can all be measured in three dimensional space using strike and dip .

2. The strike of a surface is the direction of a line formed by the intersection of a rock layer with a horizonal surface. The strike is described in terms of direction such as N 10 o W.

3. The dip is measured at right angles to the strike and is a measure of the angle at which the surface tilts relative to a horizontal surface. The dip is indicated in terms of angle and direction (e.g. 35 o E).

1. Figure 10.9 : Folds are a result of ductile deformation of rocks in response to external forces.

2. Layered rocks folded into arches are called anticlines whereas troughs are referred to as synclines .

3. Figures 10.10 & 10.11: The two sides of a fold are referred to as limbs . The two limbs come together to form an imaginary line called the fold axis. The direction in which the fold axis points indicates the strike of the fold.

4. Fig. 10.16a : A dome is an anticlinal structure where the flanking beds encircle a central point and dip radially away from it.

5. Figure 10.16b : A basin is a synclinal structure appearing as a bowl-shaped depression where rock layers dip radially towards a central point.

6. Figure 10.5 : The eroded surface of a fold appears as a series of bands of different rocks. Rock bands appearing on one side of the fold axis are duplicated on the other side. For basins and domes, strata exposed at the surface form concentric circles around a central point (Figure 10.16).

7 . Figure 10.5 : For anticlines, the surface rock exposures become progressively older towards the fold axis.

8. Fig. 10.18: Synclines show the opposite trend. Rock exposures become progressively younger towards the axis of synclines.

9. Rock layers dip away from the fold axis in anticlines, but dip toward the fold axis in synclines.

1. Figure 10.10 : A fold can be divided by an imaginary surface called the axial plane . The axial plane divides a fold as symmetrically as possible. The line formed by the intersection of the axial plane with the beds define the fold axis.

2. Figure 10.10 : The axis of a fold can be horizontal. If the axis is not horizontal, the structure is said to be a plunging fold .

3. The plunge of a fold can be described as the angle a fold axis makes with a horizontal surface. The axis of a plunging fold can therefore be described as having a certain strike (e.g. N 10 o W) and plunge (e.g. 20 o NW). Unlike dipping beds, the plunge of a fold axis is in the same direction as the strike of the axial plane.

4. Figure 10.12: Folds can be classified by their geometry with respect to their axial plane.

(a) Symmetrical Folds : Axial plane is vertical an beds dip at approximately the same angle, but in opposite directions, on either side of the plane.

(b) Asymmetrical Folds : Axial planes are inclined and one limb of the fold dips more steeply than the opposite limb, but still in opposite directions.

(c) Overturned Folds : Axial plane is inclined and both limbs of the fold dip in the same direction.

5. In general, the greater asymmetry in the fold, the more intense the deformation.

6. Figure 10.14 : When folds plunge into the earth, they essentially disappear from the surface. The curved strata comprising a plunging fold form a horseshoe or hairpin pattern on the surface where they plunge into the earth.

7. For anticlines, the horseshoe or hairpin shape closes in the direction that the anticline plunges.

8. For synclines, the horseshoe or hairpin-shape opens in the direction that the syncline plunges.

9. Figure 10.5: In the field, a geologist can reconstruct the geometry of folds by:

(a) measuring the strike and dip of various strata exposed in outcrops

(b) noting which direction the beds become younger

(c) measuring any structural deformations within the rocks.

(d) Once this information is obtained, the geologist can employ the principles of geometry and trigonometry to determine the orientation of the axial plane and also whether the fold plunges. If the fold plunges, then the plunge of the fold axis can also be determined using geometry, trigonometry and field measurements.

Rocks that undergo brittle deformation tend to fracture into joints and faults .

1. Figure 10.20 : A joint is a crack in a rock along which no appreciable movement has occurred. Strata on one side of the joint align with strata on the other side.

2. Joints can form as a result of expansion and contraction of rocks. Expansion can occur if erosion strips away the overlying rocks to exhume once deeply buried rocks. Release of confining pressure causes the exhumed rock to expand and fracture, thereby producing joints.

3. Joints aid in weathering by providing channels where water and air can reach deep into the formation.

1. Figure 10.22 : A fault is a plane of dislocation where rocks on one side of the fault have moved relative to rocks on the other side. Strata on one side of the fault plane are typically offset from strata on the opposite side.

2. Figure 10.6 : Faults can form in response to any one of the three types of forces: compression, tension and shear: The type of fault produced, however, depends on the type of force exerted.

3. A fault plane divides a rock unit into two blocks. One block is referred to as the hanging wall , the other as the footwall .

(a) The hanging wall is the block of rock above an inclined fault plane.

(b) The block of rock below an inclined fault plane constitutes the footwall.

4. Figure 10.22a : If the hanging wall slips downward relative to the footwall, the fault is defined as a normal fault.

5. Figure 10.25 : Normal faults result from tensional forces and typically form rift valleys . The down-faulted block in a rift valley is called a graben while the uplifted block is referred to as a horst .

6. Figure 10.22c : Shear forces typically produce strike-slip faults where one block slips horizontally past the another. In other words, slippage is parallel to the strike of the fault.

7. Figure 10.22b : Compressional forces typically push the hanging wall upward relative to the footwall, producing a reverse fault .

8. Figure 10.23 : A reverse fault in which the dip of the fault plane is so small as to be almost horizontal is called a thrust fault . In thrust faults, the hanging wall moves almost horizontally over the footwall.

9. Figure 10.22d : Oblique faults occur where there is both a strike-slip and dip-slip component to the fault.

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High Blood Pressure (Hypertension)

High blood pressure (hypertension) is a disease in which pressure within the arteries of the body is elevated. About 75 million people in the US have hypertension (1 in 3 adults), and only half of them are able to manage it. Many people do not know that they have high blood pressure because it often has no has no warning signs or symptoms.

Systolic and diastolic are the two readings in which blood pressure is measured. The American College of Cardiology released new guidelines for high blood pressure in 2017. The guidelines now state that blood normal blood pressure is 120/80 mmHg. If either one of those numbers is higher, you have high blood pressure.

The American Academy of Cardiology defines high blood pressure slightly differently. The AAC considers 130/80 mm Hg. or greater (either number) stage 1 hypertension. Stage 2 hypertension is considered 140/90 mm Hg. or greater.

If you have high blood pressure you are at risk of developing life threatening diseases like stroke and heart attack.

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It is common to evaluate machine learning models on a dataset using k-fold cross-validation.

The k-fold cross-validation procedure divides a limited dataset into k non-overlapping folds. Each of the k folds is given an opportunity to be used as a held-back test set, whilst all other folds collectively are used as a training dataset. A total of k models are fit and evaluated on the k hold-out test sets and the mean performance is reported.

For more on the k-fold cross-validation procedure, see the tutorial:

The k-fold cross-validation procedure can be implemented easily using the scikit-learn machine learning library.

First, let’s define a synthetic classification dataset that we can use as the basis of this tutorial.

The make_classification() function can be used to create a synthetic binary classification dataset. We will configure it to generate 100 samples each with 20 input features, 15 of which contribute to the target variable.

The example below creates and summarizes the dataset.

Running the example creates the dataset and confirms that it contains 100 samples and 10 input variables.

The fixed seed for the pseudorandom number generator ensures that we get the same samples each time the dataset is generated.

Next, we can evaluate a model on this dataset using k-fold cross-validation.

We will evaluate a LogisticRegression model and use the KFold class to perform the cross-validation, configured to shuffle the dataset and set k=10, a popular default.

The cross_val_score() function will be used to perform the evaluation, taking the dataset and cross-validation configuration and returning a list of scores calculated for each fold.

The complete example is listed below.

Running the example creates the dataset, then evaluates a logistic regression model on it using 10-fold cross-validation. The mean classification accuracy on the dataset is then reported.

Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

In this case, we can see that the model achieved an estimated classification accuracy of about 85.0 percent.

Now that we are familiar with k-fold cross-validation, let’s look at how we might configure the procedure.

You know from experience that if you drop a steel bolt in a bucket of water that it will sink like a rock to the bottom. On the other hand, you know that ships made of steel can float. How does it work?

What determines whether an object floats or sinks? It is the density (mass per unit volume) of the object compared to the density of the liquid. If the object is more dense than the fluid, it will sink. If the object is less dense than the fluid, it will float. If the object has the same density as the fluid it will neither sink nor float.

With a steel-hulled ship, it is the shape of the ship's hull that matters. On an empty ship the hull encloses a volume of air so that the total density is defined by Equation 1 below.

The ship floats because its density is less than the density of water. But when cargo or other weight is added to the ship, its density is now defined by Equation 2 below.

If too much cargo or weight is added to the ship, the density of the ship becomes greater than the density of water, and the ship sinks. Extra cargo would need to be thrown overboard in a hurry or it is time to abandon ship!

Archimedes discovered that an object placed in water displaces a volume of water. If the object is floating, the amount of water that gets displaced weighs at least as much as the object. The displaced water creates an upward force on the object, called buoyancy. The strength of this upward acting force exerted by water is equal to the weight of the water that is displaced. Whether an object sinks or floats depends on its density and the amount of water it displaces to create a strong enough buoyant force.

In this hydrodynamics science project you will make boat hulls of various shapes and sizes using simple materials (aluminum foil and tape) and determine how much weight can be supported by these hulls and how this relates to the density of water. Can you predict how many pennies each of your boats will support without sinking?

Uses for Hardness Tests

The Mohs Hardness Test is almost exclusively used to determine the relative hardness of mineral specimens. This is done as part of a mineral identification procedure in the field, in a classroom, or in a laboratory when easily identified specimens are being examined or where more sophisticated tests are not available.

In industry, other hardness tests are done to determine the suitability of a material for a specific industrial process or a specific end-use application. Hardness testing is also done in manufacturing processes to confirm that hardening treatments such as annealing, tempering, work hardening, or case hardening have been done to specification.

Information Sources
[1] Scientists Discover Material Harder Than Diamond - Lisa Zyga, website article on, February 2009.

[2] Mohs Scale of Mineral Hardness: Wikipedia article, last accessed July 2016.

[3] Material Hardness: website article, Center for Advanced Life Cycle Engineering, University of Maryland, last accessed July 2016.

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