Challenge with Geometry and Measurement" (Maximum 80 characters)

Challenge with Geometry and Measurement
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In this set of challenging geometry problems, you will solve for various measurements like lengths of lines and dimensions of shapes. From finding diagonal lengths to identifying cuboid dimensions, these problems test your spatial reasoning skills. Explore the provided diagrams and data to unveil the solutions to each unique challenge. Enhance your geometric knowledge with these engaging exercises. (Maximum 500 characters)

  • Geometry
  • Measurement
  • Math Problems
  • Spatial Reasoning
  • Challenges (Maximum 22 characters per tag)

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  1. March 2015 doc.: IEEE 11-14/0562r5 802.11ak and 802.1AC Convergence Function Date: 2014-03-10 Authors: Name Norman Finn Affiliations Address Cisco Systems Phone +1.408.526.4495 email nfinn@cisco.com 170 W Tasman Dr. San Jos CA 95134 USA 2560 55th St, Boulder, CO, 80301 +1-303-441-7553 mark.hamilton@spectralin k.com Mark Hamilton Spectralink Sli de 1 Submission Slide 1 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  2. March 2015 doc.: IEEE 11-14/0562r5 Abstract Building upon a model being proposed for the IEEE 802.11 Portal Convergence Function, this presentation carries that concept into the 802.11ak concepts, and 802.1AC considerations for these extended concepts. Sli de 2 Submission Slide 2 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  3. March 2015 doc.: IEEE 11-14/0562r5 Following are several slides from the 802.11 portal presentation (being considered in ARC, and 802.1AC) 11-14/497 Sli de 3 Submission Slide 3 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  4. March 2015 This is an example of a physical network doc.: IEEE 11-14/0562r5 802.3 802.3 AP 1 AP 2 Two physical boxes, commonly (but inaccurately) called APs, connected by an IEEE 802.3 link. Two clients of AP 1 shown, two wireless and one wired clients of AP 2 not shown. No VLANs. This example will be used repeatedly in this deck. Submission Slide 4 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  5. March 2015 Layering doc.: IEEE 11-14/0562r5 In the ISO layering model, a DATA.request is presented by a higher layer to a lower layer, and a DATA.indication is presented by a lower layer to a higher layer. In all further diagrams in this deck, the higher layer is closer to the top of the slide, and the lower layer closer to the bottom. Submission Slide 5 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  6. March 2015 Let s start at the beginning. doc.: IEEE 11-14/0562r5 indications user SAP user SAP user SAP DSAF nAP STA nAP STA nAP STA MAC PHY MAC PHY MAC PHY MAC PHY requests The medium (the ether ) Non-AP STAs DSAF = Distribution System Access Function (as opposed to the whole AP, which covers many sublayers). nAP STA == upper layers of a non-AP STA. The symbols are Service Access Points to the IEEE 802.11 Clause 5 MAC Service offered to the users of the non-AP STAs. AP STA SAP Submission Slide 6 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  7. March 2015 doc.: IEEE 11-14/0562r5 What is relationship between DSAF & DS? First interpretation: The Distribution System provides instances of a service to the DSAF(s). indications DSAF DSAF MAC PHY MAC PHY Distrib. System (DS) requests We ll call this DSAF/DS ( DSAF over DS ). (IEEE 802.11-2012 Annex R.2.2.2.3 says this, explicitly. Annex R is non-normative, but this is the only place in 802.11-2012 (that we have found) that the relationship is stated unambiguously (see e.g. Figure 4-2). Submission Slide 7 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  8. March 2015 doc.: IEEE 11-14/0562r5 What is relationship between DSAF & DS? Second interpretation: The Distribution System peers with the DSAF(s) via real or virtual links. indications DSAF DSAF Distrib. System (DS) MAC PHY MAC PHY requests We ll call this DSAF=DS ( DSAF peers with DS ). Submission Slide 8 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  9. March 2015 doc.: IEEE 11-14/0562r5 What is relationship between DSAF & DS? Third interpretation: The Distribution System utilizes instances of a service provided by the AP(s). Distrib. System (DS) indications DSAF DSAF MAC PHY MAC PHY requests We ll call this DS/DSAF ( DS over DSAF ). Submission Slide 9 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  10. March 2015 doc.: IEEE 11-14/0562r5 What the DS is NOT (I hope!) Non-useful interpretation: The Distribution System s position in the layering diagram is undefined. DSAF DSAF DS MAC PHY MAC PHY There is no place for an undefined amorphous cloudish thingamajig in the ISO layering model. Submission Slide 10 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  11. March 2015 doc.: IEEE 11-14/0562r5 This is the relationship for this deck The Distribution System provides instances of a service to the DSAF(s). indications DSAF DSAF MAC PHY MAC PHY Distrib. System (DS) requests Because this is the only one to which these authors can find a specific reference in IEEE Std 802.11. Submission Slide 11 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  12. March 2015 A standard view of that same network in 802.11 today doc.: IEEE 11-14/0562r5 AP portal MAC PHY AP MAC MAC Distribution System (DS) MAC PHY MAC PHY PHY PHY Non-AP STAs This is similar to IEEE 802.11-2012, Figure R-1, but drawn with request down indication up rigorously applied. The DS has three users, two APs and a portal, so is shown passing behind a MAC. AP STA 1 AP STA 2 unspecified 802.3 Submission Slide 12 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  13. March 2015 One possible 802.1AC-to-portal architecture doc.: IEEE 11-14/0562r5 AP portal 802.1Q bridge relay MAC MAC MAC PHY MAC PHY MAC PHY MAC PHY Distrib. System (DS) PHY PHY Non- AP station end station AP STA unspecified anything, e.g. 802.3 802.3 A connecting link is required, because the portal uses a SAP; it does not provide one. Therefore an 802.1AC convergence layer specific to 802.11 is not necessary. Submission Slide 13 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  14. March 2015 But, there is an alternate approach. doc.: IEEE 11-14/0562r5 AP portal 802.1Q bridge relay MAC MAC MAC PHY MAC PHY MAC PHY MAC PHY Distrib. System (DS) PHY PHY Non- AP station end station AP STA unspecified anything, e.g. 802.3 802.3 This interface is defined. It is the DS_SAP, illustrated in IEEE Std 802.11-2011 Figure R-1. Submission Slide 14 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  15. March 2015 So, another representation could be One example (of many) of a portal doc.: IEEE 11-14/0562r5 802.1Q bridge relay .1AC MAC AP MAC MAC MAC PHY Distrib. System (DS) PHY PHY PHY Non- AP station end station AP STA 802.3 unspecified That is, the 802.1AC Clause 12.2.1 portal convergence function is not an interface to a portal; .1AC 12.2.1, plus a bridge relay function, is an example of a portal. .1AC 12.2.1 connects the ISS to the DS_SAP. Submission Slide 15 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  16. March 2015 doc.: IEEE 11-14/0562r5 New for 802.11ak consideration Submission Slide 16 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  17. March 2015 doc.: IEEE 11-14/0562r5 Extending this to P802.11ak + P802.1Qbz 802.1Q bridge relay SAP SAP SAP SAP MA C MA C .1AC CF SAP[ ] .1AC CF SAP[ ] Conv. Funct AP AP 802.1AC 12.2.2 MAC MAC MAC PHY PHY PHY PHY PHY AP STA 1 AP STA 2 802.3 Non-AP STAs That is, 802.1AC/802.11ak are defining a SAP and a convergence function that supports multiple, logical links as seen by the Bridge, to each of the 11ak-aware non-AP endpoints. Note: SAP is a single instance, SAP[] has a port vector. Submission Slide 17 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  18. March 2015 P802.11ak and non-11ak STNs on one AP. doc.: IEEE 11-14/0562r5 AP w/Bridge and non-11ak (legacy) access Non-11ak STAs 11ak STAs Bridge 802.1AC 12.2.2 802.1AC 12.2.1 SAP SAP SAP .1AC SAP[ ] .1AC AP MAC MAC MAC MAC SAP[ ] MAC PHY DS PHY PHY PHY PHY Submission Slide 18 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  19. March 2015 P802.11ak and non-11ak STNs on two APs. doc.: IEEE 11-14/0562r5 AP w/Bridge, uses DS for non-11ak access Non- 11ak STA(s) Non- 11ak STA(s) AP w/Bridge and non-11ak (legacy) access 11ak STA(s) 11ak STA(s) Bridge Bridge isolated .1AC 12.2.2 AP .1AC 12.2.2 AP .1AC 12.2.1 MAC MAC MAC MAC MAC PHY MAC PHY DS PHY PHY PHY PHY Note that connectivity between this 11ak STN and the other stations depends on some connection between the Bridges not shown. Submission Slide 19 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  20. March 2015 P802.11ak and non-11ak STNs on two APs. doc.: IEEE 11-14/0562r5 AP w/Bridge, uses DS for non-11ak access Non- 11ak STA(s) Non- 11ak STA(s) AP w/Bridge and non-11ak (legacy) access 11ak STA(s) 11ak STA(s) Bridge Bridge .1AC 12.2.2 AP .1AC 12.2.2 AP .1AC 12.2.1 1AC 12.2.1 MAC MAC MAC MAC MAC PHY MAC PHY DS DS PHY PHY PHY PHY Now, all stations are fully connected, and the DS is split. Submission Slide 20 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  21. March 2015 P802.11ak and non-11ak STNs on two APs. doc.: IEEE 11-14/0562r5 Bridge Bridge DSX .1AC 12.2.2 AP .1AC 12.2.2 AP .1AC 12.2.1 1AC 12.2.1 MAC MAC MAC MAC MAC PHY MAC PHY DS DS PHY PHY PHY PHY It is important to understand that the DS does NOT somehow morph to include the bridge! The reason is that, once the data hits the bridge, it belongs to all bridge peers, e.g. other DSs that are using the same bridged network. The DS is not a peer of the bridge. The bridge is not part of the DS. Submission Slide 21 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  22. March 2015 P802.11ak and non-11ak STNs on two APs. doc.: IEEE 11-14/0562r5 Bridge Bridge .1AC 12.2.2 AP .1AC 12.2.2 AP .1AC 12.2.1 MAC MAC MAC MAC MAC PHY MAC PHY DS DS PHY PHY PHY PHY DS tunnel It is certainly possible to invert the stack using a DS tunnel technology (mac-in-mac, Ether-over- VPLS-over-MPLS-over-Ether, etc.) to make a single DS. But then, you re back to a single 12.2.1 portal. Submission Slide 22 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

  23. March 2015 doc.: IEEE 11-14/0562r5 To summarize A given DS has exactly one Portal to a Bridged LAN, no matter how many APs it serves. If, in order to avoid sending a packet from AP1 to AP2 and back again, you would like to have multiple Portals, you have to separate the DSs, and let the Bridge LAN move the data. Sli de 23 Submission Slide 23 Norman Finn, Cisco Systems, Mark Hamilton, Spectralink

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