In this issue we look at the Martin Luther King, Jr., Memorial and explore the challenges it had in its construction. For more math media resources, go to http://www.media4math.com

1. 12/12/11

2. MLK Memorial
This overhead view of the Memorial shows its location near the tidal basin. The
Memorial is a complex of paths and walls with the statue in the center.

3. MLK Memorial
This closer view shows the two main parts of the Memorial: The “Mountain of
Despair” and the “Stone of Hope.”

4. MLK Memorial
The “Mountain of Despair” is a large granite block with a gap in the middle. This
gap is what makes up the statue of Martin Luther King, Jr.

5. MLK Memorial
The “Stone of Hope” is a large block of granite emerging from the “Mountain of
Despair,” and out of that block of granite emerges the likeness of Martin Luther
King, Jr.

6. Sculpting with Granite
Granite is an extremely hard, durable rock that has been used sparingly throughout
history. The Egyptians created some of their monuments using granite, but because
it is difficult to sculpt, most cultures used different types of rocks.

7. Sculpting with Granite
Modern-day examples of granite structures include the Empire State Building.

8. Sculpting with Granite
The most famous modern example of a granite statue is Mt. Rushmore. The granite
face of a mountain was chiseled into the faces of Washington, Jefferson, Lincoln,
and Teddy Roosevelt.

9. MLK Memorial
Granite makes an impressive statement. To create a sculpture in granite is to
create a permanent monument that can withstand the ravages of time.

10. Rocks and Minerals
Granite is a type of rock, and rocks are made up of combinations of different
minerals. Minerals usually have a crystal structure. Rocks and minerals have
different properties, among them hardness.

11. Mohs scale Mineral
1 Talc
2 Gypsum
3 Calcite
4 Fluorite
5 Apatite
6 Orthoclase Feldspar
7 Quartz
8 Topaz
9 Corundum
10 Diamond
Rocks and Minerals
The Mohs Scale is a rough measure of the hardness of different minerals. Starting
with talc, a soft mineral, and ending with diamond, the hardest substance, the Mohs
scale tracks the hardness of key minerals.

12. MLK Memorial
The Mohs Scale is an ordinal scale where the hardness of a rock or mineral is
determined relative to two places on the scale.

13. MLK Memorial
For example, if an unknown rock can scratch feldspar and is, in turn, scratched by
quartz, then the hardness of the rock of the is between feldspar and quartz.

14. Rocks and Minerals
Since feldspar and quartz are at positions 6 and 7, respectively, on the Mohs scale,
then the unknown rock has a hardness between 6 and 7.

15. Rocks and Minerals
By convention, this rock would have a hardness of 6.5. However, since the Mohs
scale is an ordinal scale, such a measurement is not possible. All we can say is that
the hardness is somewhere between the two values.

16. Rocks and Minerals
• Granite is composed
mostly of quartz,
feldspar, and other
minerals.
• Granite should have at
least 20% quartz.

17. Rocks and Minerals
For simplicity, let’s suppose that granite is composed of just quartz and feldspar.
These minerals are adjacent to each other on the Mohs Scale. So, as with the
previous example, quartz has a hardness between 6 and 7.

18. Rocks and Minerals
Different types of granite have different proportions of quartz and feldspar,
potentially affecting the hardness of the rock. For a more accurate measure of the
hardness, we need a continuous measurement of hardness.

19. Absolute hardness scale Mineral
1 Talc
3 Gypsum
9 Calcite
21 Fluorite
48 Apatite
72 Orthoclase Feldspar
100 Quartz
200 Topaz
400 Corundum
1600 Diamond
Rocks and Minerals
There is a more accurate hardness scale that takes into account the absolute
hardness of different substances. This table shows the hardness values, and as
you can see, this is a nonlinear data set.

20. Rocks and Minerals
This is a graph of the data set. Note that it is roughly exponential.

21. Rocks and Minerals
An exponential regression shows how dramatic the growth is. The shaded region
shows the part of the scale where the hardness of granite can be found.

22. Rocks and Minerals
With a continuous hardness scale, we can see how the hardness increases from
feldspar (x = 6) to quartz (x = 7). Depending on the percentage of quartz in the
granite, the hardness can nearly double.

23. Rocks and Minerals
• Because granite is at the
higher end of hardness,
to cut granite usually
requires a diamond-
tipped cutting tool.

24. Rocks and Minerals
• What adds to granite’s
hardness is that it is
formed under intense
heat and pressure inside
the Earth, so that the
molecules of quartz and
feldspar are intermingled
and tightly knit.