Friday, June 23, 2017

Forensics.

Police, Crime Scene, Blue Light  As you know, I find the math in forensics quite interesting.  It is a way of finding information from the evidence to find the perpetrator.

On all those shows, they find the guilty person within one hour, well 45 minutes give or take a couple minutes.

In reality it can take up to a year or longer.  There was a murder in the village I live in.  A young lady was stabbed multiple times and left behind the clinic.  The police came out, interviewed everyone, gathered data, found evidence, and took forever but almost a year later, they arrested a young man for the crime. I shared one way I'd used math to prove a person not guilty of reckless driving.

Lets look at some other ways math is used in forensics to help solve crimes.

1.  One can tell an animal hair from a human hair by calculating the ratio of the diameter of medulla to the diameter of the whole hair.  If it is .5 or higher, it is animal hair.  If it is lower than .5, it is human hair.

2. Estimating the size of an individual grain of pollen using the magnification of a microscope.  The idea is to estimate how many grains of pollen will fit across and divide the size of the field of view by that and voila, you have the individual size.

3. Blood splatter uses trigonometric calculations using the height and distance to find the angle of impact.  height is opposite while distance to the splatter is adjacent.

4. Using angles, they can tell if the pelvic bones are from a male or female.  If the angle beneath the ischia bones is less than 90 degrees (forms an acute angle), it is male.  If it is greater than 90 degrees ( forms an obtuse angle), its a female. 

5. Time of death, looking at the drop in the body temperature.  For the first 12 hours, the body cools by 1.4 degrees F each hour.  After 12 hours, heat loss is calculated at .7 degrees F each hour.

6. Time of death based on insect development.  They can use the development of certain insects to approximate a time of death because insects require a certain temperature to hatch and progress from one stage to another.

If the math is packaged in something as exciting as helping to solve a crime, students are more willing to do the calculations because it is a fun and applicable situation.  I'll give some sites for creating a unit next week. 

Let me know what you think.

Thursday, June 22, 2017

Board Foot

Abstract, Antique, Backdrop, Background  I am currently working with a family member to finish off the basement.  He and his wife asked to move into the basement so they could save money and help finish the basement.

All I can say is the basement has a cement floor, lots of studs and pipes for things.  It does have a few power boxes but I need more in there.

While looking over some of those magazines on finishing this or that, I stumbled across a comment on board feet.  I'd forgotten about that measurement.  My father, being a a shop teacher, spoke about board foot and linear foot.

Technically, a board foot is a volume of 144 cubed units, such as 12 in by 12 in by 1 in while a linear foot is just the length regardless of width or depth.  Honestly, I'm never sure which unit hardware stores sell the lumber by.  The last ones I bought were sold for a flat rate, the board already cut to a certain length.  In addition, if the boards thickness is less than 3/4 inch, it is sold by the linear foot.

After some research, I'm told some stores do sell lumber by the board foot while others sell lumber by the linear foot.   Using this information and other pieces, its possible to come up with some questions students can explore.

1.  If the volume of a board foot is 144 inches square, how many different measurements can a board foot have?  Which ones are more likely than other?  Explain your choices.

2.  If you have a board that is 8 inches wide, 8 feet long, and 1 inch thick, how many board feet is that?

3.  If you have a board that is 2 inches wide, 3 inches deep, 8 feet long and costs $5.00 per board foot, how much will the board cost?

4.  If the board you have is 8 inches wide, 3/4 inch thick and 8 feet long,  how many board feet is it?  What would it cost if the hardware store charges $4.75 per board inch.

So a real life application of board feet.  let me know what you think?  Have a good day.

Wednesday, June 21, 2017

Calculating Speed from Skid Marks.

Skid Mark, Asphalt, RoadI have always loved watching television shows which involve some sort of forensics.  CSI and all its variations including NCIS captured my attention because of solving a mystery based only on evidence.

One topic they don't usually discuss is determining the speed of a vehicle based on the length of the skid marks left behind.

I have a friend who was driving home from church one day.  He came around the curve, just across the train tracks, when he hit a street sweeper that was making a U-turn in the middle of the road.  What's worse, there was a sign posted before the curve advising people to look for the flagman who was absent.

He was issued a ticket for speeding.  He came back as soon as he got a tape measure to determine the length of the marks.  He brought the information to me so I could check the officer's conclusion.  So after a bit of research and calculations, I discovered he was only going about 36.5 mph in a 35 zone. 
I used the calculation S = sqrt(30*D*f*n).  S means speed, 30 is a constant, D is the distance of the drag marks, f refers to the drag factor based on type of road, and n is the breaking efficiency in a percent.

The officer was notified of his calculation error.  I thought that would be the end of it but the officer came back with a charge of reckless driving, a charge that could result in my friend spending time in jail and loosing his license.   Add injury to insult, no lawyer would touch the case because they said the case was too absurd to be prosecuted.

The city refused to provide photos of the damage to the street cleaner.  They would not talk to the insurance company, or do much at all.  He supplied everything he could from my calculations to photos of the damage to his car, to drawings and anything else he could think of.  The insurance company was using my calculations, his pictures but the city refused to discuss it at all.

He finally went in to talk to a District Attorney to discuss his plea of not guilty with the damaged bumper in his hand. Fortunately, the D.A. had a enough classes in physics to understand my friends argument on why he was not recklessly driving.  The DA basically threw the charges out due.

This is my real life example of how my use of math in real life saved a friend from getting convicted of a fairly serious charge to being freed.  Mathematical equations do work within a real life context.  I am going to have fun having students do this in class in the fall.

Let me know what you think.  Have a good day.

Tuesday, June 20, 2017

Mapping Patterns in Crime.

Map, Attacks, Terror, Belgium, Brussels  Mathematicians love the beauty of patterns.  There are patterns in traffic flow, in nature, in crime and math is used to map those patterns showing where the crimes have been committed.

Crime analysis looks at the patterns of crimes being committed in which areas to determine the best response.
According to an article published by UCLA,  criminals are hunter gathers who hunt for criminal activities.  They follow certain patterns. 

Using mathematical modeling, the police are able to find hot spots, determine the type of hot spot, and determine the best reaction to the activity. There are two types of hot spots, the first is characterized by a small rise in activity that grows while the second is a large spike in a central location.  By knowing which type of hot spot, the police can respond appropriately so they do not cause the hot spot to move to another area without suppressing it.

In addition, they can determine if the it is a hot spot of violent crimes, burglary, or auto.  Mathematical modeling that provides this detailed information.  Apparently when a hot spot occurs for a specific crime, the chances of it occurring increase because the criminals appear to be comfortable working that area.

There are others who are investigating this type of analysis.  In the Boston area, three people including a person at MIT created a program to look at trends in crimes and discovered trends that had previously been unidentified using traditional methods.  In addition, they found several crimes that met the criteria but had not been classified prior to this.

Crime mapping provides information for three type of analysis. The first, tactical analysis, looks at the short term such as  a crime spree because they want to stop what is going on. It looks at one criminal with many targets or one target with many criminals.  It is used when an immediate response is needed.

The second, strategic crime analysis, looks at both long term and on going events.  It often focuses on areas with high crime rates and tries to find ways to decrease the crime rates. The final, administrative crime analysis, looks at the police and their deployment to determine if they are being used effectively.

The data used for these crime analysis usually come from 911 call records.  The crime is entered into the data base, if the perpetrator is arrested, if he is convicted, or put in jail, all of this is put into the data base.  The information is analyzed using mathematical modeling so one of the three type of analysis can be applied to the data.

Let me know what you think.  Have a good day and enjoy yourselves.


Monday, June 19, 2017

Cartography and Math

Italy, Alpine, Alpine Region, Map  Cartographers or map makers use quite a bit of math in the creation of maps.  I suspect if you asked most students "What math is used in map making?" they'd respond with a shrug, or its only used in the key in the corner.

In truth, cartographers use quite a bit of math.  They use math in map scales, coordinate systems, and map projection to begin with.  The math scales shows the relationship between distance on a map and distance in real life as a fraction or ratio.

The coordinate systems refers to the numerical representation of locations of places on the planet while map projection is a mathematical transformation of points from a curved surface to a flat surface.  Did you know there are at least 18 different map projections including the Mercator which is the one most people are familiar with.  They type of map projection chosen depends on what needs to be shown.  This site has a great explanation of all the different types of map projections. 

Back to the coordinate systems used in cartography.  One is the geographic coordinate system which is based on longitude and latitude to pinpoint the exact location of any place on earth.    The other type is a projected coordinate plane which takes the earths curved surface and projects it onto a coordinate system.

New Zealand Maths has a nice unit created which has students creating their own maps of the classroom complete with scale and coordinate planes to mark the location of an object on the map. The nice thing about this activity relates magnetic north to true north. 

I can hear my students telling me that paper maps are out of fashion.  Maps are on their phones, so that information is not up to date but contrary to that opinion, they are wrong.  Math is even more important because mathematical equations referred to as mathematical exact visualization are what allow you to move your view of the map around, check out streets as if you are driving down them or keep track of the various labels of building, hotels, etc.

These mathematical equations are needed so the viewer can move digital maps around and still return back to your location.  Tomorrow, I'm going to look into the use of maps and math to find patterns in crime. 

Let me know what you think.