A Collection of Sangaku Problems
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A Collection of Sangaku Problems


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  • expression écrite
  • expression écrite - matière potentielle : c.
–1– A Collection of Sangaku Problems J. Marshall Unger Department of East Asian Languages & Literatures The Ohio State University Version of 22 January 2012 PROBLEM 1: Given two lines tangent to circle (O) at B and C from a common point A, show that the circle passes through the incenter of triangle ABC.1 SOLUTION 1 (JMU): Since AB and AC are tangents, each of the base angles of the isosceles triangle ABC measures half of BOC, so the sum of half these angles is also half of BOC.
  • tablet from miyagi
  • point of tangency of the incircle of δacd 13 fukagawa
  • o3
  • altitude of the small triangle
  • top of the square
  • circles
  • right triangle
  • abc
  • o2
  • solution



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PHY 101 Lecture #26:
Solar Power
Prof. Peter R. Saulson
Office Hrs: Tues 10 –11:30, Physics 263-4, 3-5994
PHY 101 Lecture #26 Solar PowerOutline
1. How much solar power do we get?
2. Ways to capture solar power
3. Photovoltaics
4. Why does free power cost money?
5. Pricing a home photovoltaic system
PHY 101 Lecture #26 Solar PowerSolar flux
At top of atmosphere, 1400 watts/square meter.
– The atmosphere absorbs energy:
At sea level, 1000 W/m on sun-facing surface when sun is
high in the sky
– When the Sun is close to horizon, then there is
more absorption.
– Day/night cycle: power only available 1/2 time.
– Clouds reduce availability further
200 W/m on average
Syracuse more like 150 W/m .
PHY 101 Lecture #26 Solar PowerCloudiness zones
Syracuse is in one of two cloudiest zones
150 W/m on horizontal surface, averaged over full
year, over all hours of day and night
Seattle is in the other cloudy zone.
At other extreme, Arizona, New Mexico, and
parts of So. Cal and Nevada get 250 W/m .
No place in Africa is as cloudy; only Argentina
is in So. America.
PHY 101 Lecture #26 Solar PowerWays to capture solar power
Many forms of energy are essentially powered
by the sun, including:
hydro (sun powers the water cycle)
wind (sun powers air motion in atmosphere)
direct thermal capture
(Even fossil fuels are a kind of solar energy, but
being depleted at much greater rate than they
were produced -- not renewable.)
PHY 101 Lecture #26 Solar PowerEfficiency of energy capture
Plants aren’t that efficient at capturing solar
Averaged over a whole year, a cornfield captures
1.5% of solar energy as part of corn plants
(including leaves and stems.)
Some forests a bit better, deserts much worse (only
0.01% of solar energy captured in desert plants.)
PHY 101 Lecture #26 Solar PowerCan “biomass” fuel
substitute for fossil fuels?
Burning plants for fuel would be a renewable
way to capture solar energy.
“Gasohol” from corn, harvesting trees for energy
0.023% of global sunlight is captured by
To replace fossil fuel, we’d have to burn the equivalent of
more than 20% of new global plant growth each year!
PHY 101 Lecture #26 Solar PowerProspects for wind energy
Wind generators convert K of air to electrical
Need averaged winds of 11 mph to start to pay
off, reach full rated power at 28 mph.
Still, at utility scale, costs are competitive with
fossil fuels. (4 cents / kWh.)
Enough wind power in the U.S. to replace fossil
fuel, but horizon would be pretty crowded!
PHY 101 Lecture #26 Solar PowerDirect thermal capture,
a.k.a. “passive solar” power
Sunlight absorbed on dark surface is converted
directly to thermal energy.
Black surface absorbs best, can reach 90 deg C.
Used for water heaters, or to heat home.
PHY 101 Lecture #26 Solar PowerSolar generation of electricity
When light strikes properly constructed piece of
silicon, electrical voltage and current are
photovoltaic cell
Simplest are silicon crystals, but those are very
“Polycrystalline” cells work almost as well, and
are cheaper.
“Amorphous” silicon cheaper still.
PHY 101 Lecture #26 Solar Power